Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (6): 1747-1751.
Previous Articles Next Articles
Note on Quasiconvexity of Burkholder-Šverák's Function
Zhuomin Liu1(
), Xiao Zhong2,*()
1Faculty of fundamental education ,Neusoft institute Guangdong Guangdong foshan 528200 2School of Mathematics ,Sun Yat-sen University Guangzhou 510275
-
Received:2025-09-01Revised:2025-10-10Online:2025-12-26Published:2025-11-18 -
Contact:Xiao Zhong E-mail:lzhuomin@outlook.com;zhongx@mail.sysu.edu.cn
CLC Number:
- O175
Cite this article
Zhuomin Liu, Xiao Zhong. Note on Quasiconvexity of Burkholder-Šverák's Function[J].Acta mathematica scientia,Series A, 2025, 45(6): 1747-1751.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| [1] |
Astala K, Iwaniec T, Prause I, Saksman E. Burkholder integrals, Morrey's problem and quasiconformal mappings. J Amer Math Soc, 2012, 25(2): 507-531
doi: 10.1090/S0894-0347-2011-00718-2 |
| [2] | Baernstein II A, Montgomery-Smith S J. Some conjectures about integral means of $\partial f$ and $\bar\partial f$. Acta Universitatis Upsdiensis, 1999, 64: 92-109 |
| [3] |
Ball J M. Convexity conditions and existence theorems in nonlinear elasticity. Arch Rational Mech Anal, 1978, 63: 337-403
doi: 10.1007/BF00279992 |
| [4] | Bañuelos R, Wang G. Sharp inequalities for martingales with applications to the Beurling-Ahfors and Riesz tranforms. Duke Math J, 1995, 80: 575-600 |
| [5] | Burkholder D L. Differential subordination of harmonic functions and martingales.//García-Cuerva J. Harmonic Analysis and Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989, 1384: 1-23 |
| [6] | Faraco D, Zhong X. Quasiconvex functions and Hessian equations. Arch Rational Mech Anal, 2003 168: 24-252 |
| [7] | Iwaniec T. Extremal inequalities in Sobolev spaces and quasiconformal mappings. Z Anal Anwendungen, 1982, 1: 1-16 |
| [8] |
Morrey C B. Quasi-convexity and the lower semicontinuity of multiple integrals. Pacific J Math, 1952, 2: 25-53
doi: 10.2140/pjm |
| [9] |
Šverák V. Examples of rank-one convex functions. Proc Roy Soc Edinburgh, 1990, 114(3/4): 237-242
doi: 10.1017/S0308210500024410 |
| [10] |
Šverák V. Rank-one convexity does not imply quasiconvexity. Proc Roy Soc Edinburgh, 1992, 120(1/2): 185-189
doi: 10.1017/S0308210500015080 |
| [11] |
Šverák V. New examples of quasiconvex functions. Arch Rational Mech Anal, 1992, 119(4): 293-300
doi: 10.1007/BF01837111 |
| [12] | Volberg A. Ahlfors-Beurling operator on radial functions. arXiv: 1203.2291, 2012 |
| [1] | Xiao Luo, Xi Qin. Limiting Properties of Ground States for the Schrödinger Equation with Mixed Repulsive Nonlinear Terms [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1942-1960. |
| [2] | Mengxia Wu, Tao Yang, Hua Zhang. Another Proof on the Existence of Normalized Solution to a Fourth-Order Schrödinger Equation [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1928-1941. |
| [3] | Ke Jin, Lushun Wang. Infinitely Many Solutions for Some Biharmonic Problems with Navier Boundary Condition [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1875-1887. |
| [4] | Xiaoming An, Yining Fang, Zhengchang Jin. Ground State Solution for Fractional Schrödinger Equations with General Logarithmic Nonlinear Terms [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1839-1853. |
| [5] | Xiaohui Yu. Weighted Pucci Operator and Nonlinear Liouville Theorems [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1814-1824. |
| [6] | Changlin Xiang, Jie Wang, Binhang Zhang, Yanping Zhou. Borderline Regularity and Compactness Theory for An Even Order Elliptic Systems [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1806-1813. |
| [7] | Huifang Jia, Xiangyi Ye. Normalized Solutions to the Schrödinger Equation with Forcing Perturbation Term [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1791-1805. |
| [8] | Changjian Wang, Gaofeng Zheng. Convergence of Solutions to Dirichlet Problem of Parabolic Allen-Cahn Equation [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1768-1790. |
| [9] | Xiaochun Liu, Liwei Wang. The Existence of Solutions to a Class of Fourth-Ordered Kirchhoff-Type Equations with Critical Growth [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1752-1767. |
| [10] | Huan Luo, Haoguang Li. Global Well-Posedness and Optimal Decay for the Lower Regularity Solution of Boltzmann Equation [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1854-1874. |
| [11] | Hongyu Ye. The Existence of Normalized Solutions for the Quasilinear Schrödinger Equations with $L^2$-Subcritical General Nonlinearity [J]. Acta mathematica scientia,Series A, 2025, 45(6): 1907-1927. |
| [12] | Ruiyao Xue, Guolin Hou. The Fine Pseudo-Spectra of a Class of Operator Pencils with Minimal Pseudo-Spectra [J]. Acta mathematica scientia,Series A, 2025, 45(5): 1392-1404. |
| [13] | Chao Zhu, Qingming Hao, Zhigang Pan, Yanhua Wang. Steady-State Bifurcation to a Class of Extended Fisher-Kolmogorov System with Cooperative and Self-Limiting Effects [J]. Acta mathematica scientia,Series A, 2025, 45(5): 1432-1443. |
| [14] | Junyuan Deng, Junhao Zhang. Stability to a Hyperbolic System with Cattaneo's Law in the Half Space [J]. Acta mathematica scientia,Series A, 2025, 45(5): 1444-1462. |
| [15] | Liutao Guo, Chaojiang Xu. Analytical Smoothing Effect on Cauchy Problem of Nonlinear Hyperbolic Schrödinger Equation [J]. Acta mathematica scientia,Series A, 2025, 45(5): 1463-1476. |
|
||