拟微分算子在$H^p(\omega)$上的有界性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 303-312.

拟微分算子在$H^p(\omega)$上的有界性

温泳铭¹(),侯宪明^2,*()

¹ 闽南师范大学数学与统计学院福建漳州 363000
² 临沂大学数学与统计学院山东临沂 276005

收稿日期:2020-09-17 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 侯宪明 E-mail:wenyongmingxmu@163.com;houxianming37@163.com
作者简介:温泳铭, E-mail: wenyongmingxmu@163.com
基金资助:
闽南师范大学校长基金(KJ2020020);福建省中青年教师教育科研项目(JAT200331)

The Boundedness of Pseudodifferential Operators on $H^p(\omega)$

Yongming Wen¹(),Xianming Hou^2,*()

¹ School of Mathematics and Statistics, Minnan Normal University, Fujian Zhangzhou 363000
² School of Mathematics and Statistics, Linyi University, Shandong Linyi 276005

Received:2020-09-17 Online:2021-04-26 Published:2021-04-29
Contact: Xianming Hou E-mail:wenyongmingxmu@163.com;houxianming37@163.com
Supported by:
the President's Fund of Minnan Normal University(KJ2020020);the Scientific Research Project of the Education Department of Fujian Province(JAT200331)

摘要/Abstract

摘要：

该文给出了拟微分算子$T_\sigma$在加权Hardy空间$H^p(\omega)$上的有界性，改进和推广了已有的相关结果.

关键词: 拟微分算子, 权, Hardy空间

Abstract:

This paper gives the boundedness of a class of pseudodifferential operators $T_\sigma$ on weighted Hardy spaces $H^p(\omega)$, which improves the previous known results.

Key words: Pseudodifferential operator, Weight, Hardy spaces

中图分类号:

O174.2

温泳铭,侯宪明. 拟微分算子在$H^p(\omega)$上的有界性[J]. 数学物理学报, 2021, 41(2): 303-312.

Yongming Wen,Xianming Hou. The Boundedness of Pseudodifferential Operators on $H^p(\omega)$[J]. Acta mathematica scientia,Series A, 2021, 41(2): 303-312.

参考文献

1	Alvarez J , Hounie J . Estimates for the kernel and continuity properties of pseudo-differential operators. Ark Mat, 1990, 28 (1/2): 1- 22
2	Atiyah M F , Singer I M . The index of elliptic operators I. Ann of Math, 1968, 87 (3): 484- 530
3	Beltran D . Control of pseudo-differential operators by maximal functions via weighted inequalities. Trans Amer Math Soc, 2019, 371 (5): 3117- 3143
4	Beltran D , Cladek L . Sparse bounds for pseudo-differential operators. J Anal Math, 2020, 140 (1): 89- 116
5	Bownik M , Li B D , Yang D C , et al. Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ Math J, 2008, 57 (7): 3065- 3100
6	Cao M M , Xue Q Y , Yabuta K . Weak and strong type estimates for the multilinear pseudo-differential operators. J Funct Anal, 2020, 278 (10): 46
7	Chanillo S , Torchinsky A . Sharp function and weighted $L.p$ estimates for a class of pseudo-differential operators. Ark Mat, 1986, 24 (1): 1- 25
8	Coifman R R . A real variable characterization of $H^p$. Studia Math, 1974, 51, 269- 274
9	Coifman R R , Rochberg R , Weiss G . Factorization theorems for Hardy spaces in several variables. Ann of Math (2), 1976, 103 (3): 611- 635
10	Coifman R R , Weiss G . Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83 (4): 569- 645
11	Deng Y L , Long S C . Pseusodifferential operators on weighted Hardy spaces. J Funct Spaces, 2020,
12	Fefferman C . $L^p$ bounds for pseudo-differential operators. Israel J Math, 1973, 14, 413- 417
13	Fefferman C , Stein E M . $H^p$ spaces of several variables. Acta Math, 1972, 129, 137- 193
14	García-Cuerva L . Weighted $H^p$ Spaces. Warszawa: Polish Scientific Publishers, 1979,
15	H?rmander L . Pseudo-differential operators and non-elliptic boundary problems. Ann of Math (2), 1966, 83, 129- 209
16	H?rmander L . On the $L^2$ continuity of pseudo-differential operators. Comm Pure Appl Math, 1971, 24, 529- 535
17	Hounie J , Kapp R A d S . Pseudo-differential operators on local Hardy spaces. J Fourier Anal Appl, 2009, 15 (2): 153- 178
18	Kohn J J , Nirenberg L . An algebra of pseudo-differential operators. Comm Pure Appl Math, 1965, 18, 269- 305
19	Michalowski N , Rule D J , Staubach W . Weighted norm inequalities for pseudo-differential operators defined by amplitudes. J Funct Anal, 2010, 258 (12): 4183- 4209
20	Michalowski N , Rule D J , Staubach W . Weighted $L^p$ boundedness of pseudo-differential operators and applications. Canad Math Bull, 2012, 55 (3): 555- 570
21	Str?mberg J , Torchinsky A . Weighted Hardy spaces. New York: Springer-Verlag, 1989
22	Xiao J W , Jiang Y S , Gao W H . Bilinear pseudo-differential operators on local Hardy spaces. Acta Math Sin (Engl Ser), 2012, 28 (2): 255- 266
23	Yabuta K . A note on weighted norm inequalities for pseudodifferential operators. Bull Fac Sci Ibaraki Univ Ser A, 1986, 18, 7- 12

[1]	胡浩, 叶善力. Hilbert 矩阵算子在对数加权 Bergman 空间上的范数[J]. 数学物理学报, 2025, 45(5): 1405-1416.
[2]	郭留涛, 徐超江. 非线性双曲型 Schrödinger 方程柯西问题的解析光滑效应[J]. 数学物理学报, 2025, 45(5): 1463-1476.
[3]	何曼露, 黎定仕. 加权空间中非自治离散修正 Swift-Hohenberg 方程的统计解[J]. 数学物理学报, 2025, 45(5): 1586-1601.
[4]	李子燕, 陶祥兴. 基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画[J]. 数学物理学报, 2025, 45(3): 665-686.
[5]	王占锋, 王静瑶, 吴耀华, 明瑞星. 双删失纵向数据的复合 Tobit 分位数亚组分析回归方法[J]. 数学物理学报, 2025, 45(3): 902-918.
[6]	杨贵诚, 温杨哲, 毛井. 加权Laplace算子Dirichlet特征值问题的一个万有不等式及其应用[J]. 数学物理学报, 2025, 45(1): 54-73.
[7]	范甜甜, 汤京永, 周金川. 求解加权水平线性互补问题的非单调光滑非精确牛顿法[J]. 数学物理学报, 2025, 45(1): 165-179.
[8]	洪勇, 赵茜. 构建超齐次核有界离散算子的参数条件及算子范数估计[J]. 数学物理学报, 2024, 44(4): 837-846.
[9]	王瑶瑶, 吕玫钏, 李文明. 高维 Hardy 算子及其交换子的双权不等式[J]. 数学物理学报, 2024, 44(3): 539-546.
[10]	王攀星, 梁玉霞, 庞淞月. 哈代希尔伯特空间上复 Volterra 算子的数值域[J]. 数学物理学报, 2024, 44(2): 276-285.
[11]	程鑫, 张婧. 单边算子的多线性交换子在 Triebel-Lizorkin 空间上的加权有界性[J]. 数学物理学报, 2024, 44(1): 50-59.
[12]	李文鑫,连攀,梁玉霞. Fock 型空间上的 Schödinger 测不准关系[J]. 数学物理学报, 2023, 43(5): 1321-1332.
[13]	王梓欢,王超. 一类双质子弱耦合碰撞系统的对称周期解[J]. 数学物理学报, 2023, 43(5): 1427-1439.
[14]	邹天芳,赵才地. 加权空间中一阶格点系统的统计解及其 Kolmogorov 熵[J]. 数学物理学报, 2023, 43(5): 1559-1574.
[15]	姚落根,刘欢,陈琪琼. VG扭曲算子在期权定价中的应用[J]. 数学物理学报, 2023, 43(5): 1575-1584.