Boundedness of pseudodifferential operators on modulation spaces

被引：21

作者：

Czaja, W ^{[1
]}

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 284卷 / 01期

关键词：

Gabor transform; short-time Fourier transform; modulation spaces; pseudodifferential operators;

D O I：

10.1016/S0022-247X(03)00364-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study classes of pseudodifferential operators which are bounded on large collections of modulation spaces. The conditions on the operators are stated in terms of the L-p,L-q estimates for the continuous Gabor transforms of their symbols. In particular, we show how these classes are related to the class of operators of Grochenig and Heil, which is bounded on all modulation spaces. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：389 / 396

页数：8

共 50 条

[1] THE BOUNDEDNESS OF PSEUDODIFFERENTIAL-OPERATORS ON MODULATION SPACES
TACHIZAWA, K
[J]. MATHEMATISCHE NACHRICHTEN, 1994, 168 : 263 - 277
[2] Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces
Lorenza D’Elia
S. Ivan Trapasso
[J]. Journal of Pseudo-Differential Operators and Applications, 2018, 9 : 881 - 890
[3] Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces
D'Elia, Lorenza
Trapasso, S. Ivan
[J]. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2018, 9 (04) : 881 - 890
[4] ON BOUNDEDNESS OF PSEUDODIFFERENTIAL OPERATORS IN WEIGHT SPACES
KHAIKIN, YE
[J]. DOKLADY AKADEMII NAUK SSSR, 1970, 190 (02): : 289 - &
[5] Boundedness of Pseudodifferential Operators on Banach Function Spaces
Karlovich, Alexei Yu.
[J]. OPERATOR THEORY, OPERATOR ALGEBRAS AND APPLICATIONS, 2014, 242 : 185 - 195
[6] Modulation spaces and pseudodifferential operators
Karlheinz Gröchenig
Christopher Heil
[J]. Integral Equations and Operator Theory, 1999, 34 : 439 - 457
[7] Pseudodifferential operators on modulation spaces
Labate, D
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 262 (01) : 242 - 255
[8] Modulation spaces and pseudodifferential operators
Gröchenig, K
Heil, C
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1999, 34 (04) : 439 - 457
[9] Boundedness and Fredholmness of pseudodifferential operators in variable exponent spaces
Rabinovich, Vladimir
Samko, Stefan
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2008, 60 (04) : 507 - 537
[10] Boundedness and Fredholmness of Pseudodifferential Operators in Variable Exponent Spaces
Vladimir Rabinovich
Stefan Samko
[J]. Integral Equations and Operator Theory, 2008, 60 : 507 - 537

← 1 2 3 4 5 →