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一年内发表的文章 |  两年内 |  三年内 |  全部 Please wait a minute... 选择: 合并摘要 下载引用 EndNote Reference Manager ProCite BibTeX RefWorks 显示/隐藏图片 Select 1. BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS Boyong Chen, Liangying Jiang 数学物理学报(英文版)    2024, 44 (3): 789-809.   DOI: 10.1007/s10473-024-0301-1 摘要 （208）            收藏 In this article, we investigate the (big) Hankel operator $H_f$ on the Hardy spaces of bounded strongly pseudoconvex domains $\Omega$ in $\mathbb{C}^n$. We observe that $H_f$ is bounded on $H^p(\Omega)$ ($1< p<\infty$) if $f$ belongs to BMO and we obtain some characterizations for $H_f$ on $H^2(\Omega)$ of other pseudoconvex domains. In these arguments, Amar's $L^p$-estimations and Berndtsson's $L^2$-estimations for solutions of the $\bar{\partial}_b$-equation play a crucial role. In addition, we solve Gleason's problem for Hardy spaces $H^p(\Omega)$ ($1\le p\le\infty$) of bounded strongly pseudoconvex domains. 参考文献 | 相关文章 | 多维度评价 Select 2. GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES Min He, Maofa Wang, Jiale Chen 数学物理学报(英文版)    2025, 45 (2): 291-309.   DOI: 10.1007/s10473-025-0201-z 摘要 （198）            收藏 In this paper, we study composition operators on weighted Bergman spaces of Dirichlet series. We first establish some Littlewood-type inequalities for generalized mean counting functions. Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series. The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained. 参考文献 | 相关文章 | 多维度评价 Select 3. LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY* Zhongmin Qian, Xingcheng Xu 数学物理学报(英文版)    2024, 44 (5): 1609-1638.   DOI: 10.1007/s10473-024-0501-8 摘要 （158）            收藏 This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering. 参考文献 | 相关文章 | 多维度评价 Select 4. THE GRADIENT ESTIMATE OF SUBELLIPTIC HARMONIC MAPS WITH A POTENTIAL Han Luo 数学物理学报(英文版)    2024, 44 (4): 1189-1199.   DOI: 10.1007/s10473-024-0401-y 摘要 （152）            收藏 In this paper, we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations. Under some suitable conditions, we give the gradient estimates of these maps and establish a Liouville type result. 参考文献 | 相关文章 | 多维度评价 Select 5. FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY Ang FU, Mingjin LI, Di YANG 数学物理学报(英文版)    2024, 44 (2): 405-419.   DOI: 10.1007/s10473-024-0201-4 录用日期: 2023-10-16 预出版日期: 2023-12-06 摘要 （133）      PDF       收藏 For an arbitrary solution to the Volterra lattice hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method. In this paper, we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent; based on this we obtain a new formula for the $k$-point functions for the Volterra lattice hierarchy in terms of wave functions. As an application, we give an explicit formula of $k$-point functions for the even GUE (Gaussian Unitary Ensemble) correlators. 参考文献 | 相关文章 | 多维度评价 Select 6. ON THE SOBOLEV DOLBEAULT COHOMOLOGY OF A DOMAIN WITH PSEUDOCONCAVE BOUNDARIES Jian CHEN 数学物理学报(英文版)    2024, 44 (2): 431-444.   DOI: 10.1007/s10473-024-0203-2 录用日期: 2023-10-16 摘要 （128）      PDF       收藏 In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type $\Omega=\widetilde{\Omega} \backslash \overline{\bigcup_{j=1}^{m}\Omega_j}$, where $\widetilde{\Omega}$ and $\{\Omega_j\}_{j=1}^m\Subset\widetilde{\Omega}$ are bounded pseudoconvex domains in $\mathbb{C}^n$ with smooth boundaries, and $\overline{\Omega}_1,\cdots,\overline{\Omega}_m$ are mutually disjoint. The main results can also be quickly obtained by virtue of [5]. 参考文献 | 相关文章 | 多维度评价 Select 7. THE WEIGHTED KATO SQUARE ROOT PROBLEM OF ELLIPTIC OPERATORS HAVING A BMO ANTI-SYMMETRIC PART Wenxian MA, Sibei YANG 数学物理学报(英文版)    2024, 44 (2): 532-550.   DOI: 10.1007/s10473-024-0209-9 摘要 （127）      PDF       收藏 Let $n\ge2$ and let $L$ be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a $\mathrm{BMO}$ anti-symmetric part in $\mathbb{R}^n$. In this article, we consider the weighted Kato square root problem for $L$. More precisely, we prove that the square root $L^{1/2}$ satisfies the weighted $L^p$ estimates $\|L^{1/2}(f)\|_{L^p_\omega(\mathbb{R}^n)}\le C\|\nabla f\|_{L^p_\omega (\mathbb{R}^n;\mathbb{R}^n)}$ for any $p\in(1,\infty)$ and $\omega\in A_p{(\mathbb{R}^n)}$ (the class of Muckenhoupt weights), and that $\|\nabla f\|_{L^p_\omega(\mathbb{R}^n;\mathbb{R}^n)}\le C\|L^{1/2}(f)\|_{L^p_\omega(\mathbb{R}^n)}$ for any $p\in(1,2+\varepsilon)$ and $\omega\in A_p(\mathbb{R}^n)\cap RH_{(\frac{2+\varepsilon}{p})'}(\mathbb{R}^n)$ (the class of reverse Hölder weights), where $\varepsilon\in(0,\infty)$ is a constant depending only on $n$ and the operator $L$, and where $(\frac{2+\varepsilon}{p})'$ denotes the Hölder conjugate exponent of $\frac{2+\varepsilon}{p}$. Moreover, for any given $q\in(2,\infty)$, we give a sufficient condition to obtain that $\|\nabla f\|_{L^p_\omega(\mathbb{R}^n;\mathbb{R}^n)} \le C\|L^{1/2}(f)\|_{L^p_\omega(\mathbb{R}^n)}$ for any $p\in(1,q)$ and $\omega\in A_p(\mathbb{R}^n)\cap RH_{(\frac{q}{p})'}(\mathbb{R}^n)$. As an application, we prove that when the coefficient matrix $A$ that appears in $L$ satisfies the small $\mathrm{BMO}$ condition, the Riesz transform $\nabla L^{-1/2}$ is bounded on $L^p_\omega(\mathbb{R}^n)$ for any given $p\in(1,\infty)$ and $\omega\in A_p(\mathbb{R}^n)$. Furthermore, applications to the weighted $L^2$-regularity problem with the Dirichlet or the Neumann boundary condition are also given. 参考文献 | 相关文章 | 多维度评价 Select 8. THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE Ke JIN, Ying SHI, Huafei XIE 数学物理学报(英文版)    2024, 44 (2): 583-608.   DOI: 10.1007/s10473-024-0212-1 摘要 （123）      PDF       收藏 In this paper, we consider the semilinear elliptic equation systems $ \left\{\begin{array}{ll} -\Delta u+u=\alpha Q_{n}(x)|u|^{\alpha-2}|v|^{\beta}u &\mbox{in}\hspace{1.14mm} \mathbb{R}^{N},\\ -\Delta v+v=\beta Q_{n}(x)|u|^{\alpha}|v|^{\beta-2}v &\mbox{in}\hspace{1.14mm} \mathbb{R}^{N}, \end{array} \right. $ where $N\geqslant 3$, $\alpha$, $\beta>1$, $\alpha+\beta<2^{*}$, $2^{*}=\frac{2N}{N-2}$ and $Q_{n}$ are bounded given functions whose self-focusing cores $\{x\in\mathbb{R}^N|Q_n(x)>0\}$ shrink to a set with finitely many points as $n\rightarrow\infty$. Motivated by the work of Fang and Wang [13], we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points, and we build the localized concentrated bound state solutions for the above equation systems. 参考文献 | 相关文章 | 多维度评价 Select 9. STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION Mohsan Raza, Hadiqa Zahid, Jinlin Liu 数学物理学报(英文版)    2024, 44 (4): 1244-1270.   DOI: 10.1007/s10473-024-0404-8 摘要 （119）            收藏 Let $q_{\lambda }\left( z\right) =1+\lambda \sinh (\zeta ),\ 0<\lambda <1/\sinh \left( 1\right) $ be a non-vanishing analytic function in the open unit disk. We introduce a subclass $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ of starlike functions which contains the functions $\mathfrak{f}$ such that $z\mathfrak{f}^{\prime }/\mathfrak{f}$ is subordinated by $q_{\lambda }$. We establish inclusion and radii results for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $. We also find a sharp bound for the third Hankel determinant for the case $\lambda =1/2$. 参考文献 | 相关文章 | 多维度评价 Select 10. SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES Yong CHEN, Young Joo LEE 数学物理学报(英文版)    2024, 44 (3): 810-822.   DOI: 10.1007/s10473-024-0302-0 摘要 （117）            收藏 We consider dual Toeplitz operators on the orthogonal complements of the ock-Sobolev spaces of all nonnegative real orders. First, for symbols in a certain class containing all bounded functions, we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero. Next, for bounded symbols, we construct a symbol map and exhibit a short exact sequence associated with the $C^*$-algebra generated by all dual Toeplitz operators with bounded symbols. 参考文献 | 相关文章 | 多维度评价 Select 11. MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS Quanquan Yao, Peiyong Zhu 数学物理学报(英文版)    2024, 44 (4): 1200-1228.   DOI: 10.1007/s10473-024-0402-x 摘要 （116）            收藏 Let $(X,T)$ be a linear dynamical system, where $X$ is a Banach space and $T:X \to X$ is a bounded linear operator. This paper obtains that $(X,T)$ is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if $(X,T)$ is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity. 参考文献 | 相关文章 | 多维度评价 Select 12. ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA* Zhanjie SONG, Jiaxing ZHANG 数学物理学报(英文版)    2024, 44 (5): 1984-1996.   DOI: 10.1007/s10473-024-0521-4 摘要 （116）            收藏 In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs. 参考文献 | 相关文章 | 多维度评价 Select 13. THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT Xiaoyu XIA, Litan YAN, Qing YANG 数学物理学报(英文版)    2024, 44 (2): 671-685.   DOI: 10.1007/s10473-024-0216-x 摘要 （113）      PDF       收藏 Let $B^{H} $ be a fractional Brownian motion with Hurst index $\frac{1}{2}\leq H< 1$. In this paper, we consider the equation (called the Ornstein-Uhlenbeck process with a linear self-repelling drift) $\begin{equation*} {\rm d}X_{t}^{H}={\rm d}B_{t}^{H}+\sigma X_t^{H}{\rm d}t+\nu {\rm d}t-\theta \left(\int_{0}^{t}(X_t^{H}-X_{s}^{H}){\rm d}s\right){\rm d}t, \end{equation*} $ where $\theta<0$, $\sigma,\nu \in \mathbb{R}$. The process is an analogue of {self-attracting} diffusion (Cranston, Le Jan. Math Ann, 1995, 303: 87-93). Our main aim is to study the large time behaviors of the process. We show that the solution $X^H$ diverges to infinity as $t$ tends to infinity, and obtain the speed at which the process $X^H$ diverges to infinity as $t$ tends to infinity. 参考文献 | 相关文章 | 多维度评价 Select 14. BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS Yiting WU 数学物理学报(英文版)    2024, 44 (2): 609-631.   DOI: 10.1007/s10473-024-0213-0 摘要 （111）      PDF       收藏 In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition $CDE'(n,0)$, the polynomial volume growth of degree $m$, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133). 参考文献 | 相关文章 | 多维度评价 Select 15. SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION Changlin XIANG, Gaofeng ZHENG 数学物理学报(英文版)    2024, 44 (2): 420-430.   DOI: 10.1007/s10473-024-0202-3 录用日期: 2023-10-16 预出版日期: 2023-12-06 摘要 （108）      PDF       收藏 This paper is a continuation of recent work by Guo-Xiang-Zheng[10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation $\begin{equation*} \Delta^{2}u=\Delta(V\nabla u)+{\rm div}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in }B^{4},\end{equation*}$ under the smallest regularity assumptions of $V,w,\omega, F$, where $f$ belongs to some Morrey spaces. This work was motivated by many geometrical problems such as the flow of biharmonic mappings. Our results deepens the $L^p$ type regularity theory of [10], and generalizes the work of Du, Kang and Wang [4] on a second order problem to our fourth order problems. 参考文献 | 相关文章 | 多维度评价 Select 16. THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARD POTENTIAL Lvqiao LIU, Juan ZENG 数学物理学报(英文版)    2024, 44 (2): 455-473.   DOI: 10.1007/s10473-024-0205-0 录用日期: 2023-10-16 预出版日期: 2023-12-06 摘要 （107）      PDF       收藏 In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary $L^2$ weighted estimates. 参考文献 | 相关文章 | 多维度评价 Select 17. THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX* Yinzheng Sun, Aifang Qu, Hairong Yuan 数学物理学报(英文版)    2024, 44 (1): 37-77.   DOI: 10.1007/s10473-024-0102-6 摘要 （107）      PDF       收藏 We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux, more specifically, for pressureless flow on the left and polytropic flow on the right separated by a discontinuity $x=x(t)$. We prove that this problem admits global Radon measure solutions for all kinds of initial data. The over-compressing condition on the discontinuity $x=x(t)$ is not enough to ensure the uniqueness of the solution. However, there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve $x=x(t)+0$, in addition to the full adhesion condition on its left-side. As an application, we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas. In particular, we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas. This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field. 参考文献 | 相关文章 | 多维度评价 Select 18. APPROXIMATION PROBLEMS ON THE SMOOTHNESS CLASSES* Yongping LIU, Man LU 数学物理学报(英文版)    2024, 44 (5): 1721-1734.   DOI: 10.1007/s10473-024-0505-4 摘要 （106）            收藏 This paper investigates the relative Kolmogorov $n$-widths of $2\pi$-periodic smooth classes in $\widetilde{L}_{q}$. We estimate the relative widths of $\widetilde{W}^{r} H_{p}^{\omega}$ and its generalized class $K_{p}H^{\omega}(P_{r})$, where $K_{p}H^{\omega}(P_{r})$ is defined by a self-conjugate differential operator $P_{r}(D)$ induced by $P_{r}(t):= t^{\sigma} \Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} > 0,~j=1, 2 ,\cdots, l,~l \geq 1,~\sigma \geq 1,~r=2l+\sigma .$ Also, the modulus of continuity of the $r$-th derivative, or $r$-th self-conjugate differential, does not exceed a given modulus of continuity $\omega$. Then we obtain the asymptotic results, especially for the case $p=\infty , 1\leq q \leq \infty$. 参考文献 | 相关文章 | 多维度评价 Select 19. CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY* Thomas E. Cecil 数学物理学报(英文版)    2024, 44 (1): 1-36.   DOI: 10.1007/s10473-024-0101-7 摘要 （106）      PDF       收藏 This is a survey of local and global classification results concerning Dupin hypersurfaces in $S^n$ (or ${\bf R}^n$) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of $S^n$ (or ${\bf R}^n$), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties. 参考文献 | 相关文章 | 多维度评价 Select 20. THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS Zihou ZHANG, Jing ZHOU 数学物理学报(英文版)    2024, 44 (2): 445-454.   DOI: 10.1007/s10473-024-0204-1 录用日期: 2023-10-16 预出版日期: 2023-12-06 摘要 （105）      PDF       收藏 In this paper, we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property. We introduce the concepts of the weak$^*$-weak denting point and the weak$^*$-weak$^*$ denting point of a set. These are the generalizations of the weak$^*$ denting point of a set in a dual Banach space. By use of the weak$^*$-weak denting point, we characterize the very smooth space, the point of weak$^*$-weak continuity, and the extreme point of a unit ball in a dual Banach space. Meanwhile, we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces. Moreover, we define the nearly weak dentability in Banach spaces, which is a generalization of near dentability. We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability. We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the $w$-strong proximinality of every closed convex subset of Banach spaces. 参考文献 | 相关文章 | 多维度评价