Weighted norm inequalities for fractional operators

被引：20

作者：

Auscher, Pascal ^{[1
,2
]}

Maria Martell, Jose ^{[3
]}

机构：

[1] Univ Paris 11, F-91405 Orsay, France

[2] CNRS, UMR 8628, F-91405 Orsay, France

[3] CSIC, Inst Ciencias Matemat, UAM UCM UC3M, E-28006 Madrid, Spain

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2008年 / 57卷 / 04期

关键词：

Muckenhoupt weights; elliptic operators in divergence form; fractional operators; commutators with bounded mean oscillation functions; good-lambda inequalities;

D O I：

10.1512/iumj.2008.57.3236

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-A method that does not use any size or smoothness estimates for the kernels.

引用

页码：1845 / 1869

页数：25

共 50 条

[1] Weighted Norm Inequalities for Fractional Bergman Operators
Sehba, Benoit F.
[J]. CONSTRUCTIVE APPROXIMATION, 2020, 51 (01) : 225 - 245
[2] Weighted Norm Inequalities for Fractional Bergman Operators
Benoît F. Sehba
[J]. Constructive Approximation, 2020, 51 : 225 - 245
[3] Weighted norm inequalities related to fractional Schrodinger operators
Wang, Zhiyong
Li, Pengtao
Liu, Yu
[J]. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2023, 14 (04)
[4] Weighted norm inequalities for geometric fractional maximal operators
David Cruz-Uribe
C. J. Neugebauer
V. Olesen
[J]. Journal of Fourier Analysis and Applications, 1999, 5 : 45 - 66
[5] Weighted norm inequalities for geometric fractional maximal operators
Cruz-Uribe, D
Neugebauer, CJ
Olesen, V
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1999, 5 (01) : 45 - 66
[6] Weighted norm inequalities for fractional integral operators with rough kernel
Ding, Y
Lu, SZ
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1998, 50 (01): : 29 - 39
[7] Weighted norm inequalities for multilinear fractional operators on Morrey spaces
Iida, Takeshi
Sato, Enji
Sawano, Yoshihiro
Tanaka, Hitoshi
[J]. STUDIA MATHEMATICA, 2011, 205 (02) : 139 - 170
[8] Weighted norm inequalities related to fractional Schrödinger operators
Zhiyong Wang
Pengtao Li
Yu Liu
[J]. Journal of Pseudo-Differential Operators and Applications, 2023, 14
[9] Weighted norm inequalities for operators of potential type and fractional maximal functions
Sawyer, ET
Wheeden, RL
Zhao, SY
[J]. POTENTIAL ANALYSIS, 1996, 5 (06) : 523 - 580
[10] Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces
Yueshan Wang
[J]. Analysis in Theory and Applications, 2017, 33 (02) : 93 - 109

← 1 2 3 4 5 →