Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces

作     者：Cordero, Elena D'Elia, Lorenza Trapasso, S. Ivan 

作者机构：Univ Torino Dipartimento Matemat Via Carlo Alberto 10 I-10123 Turin Italy Politecn Torino Dipartimento Sci Matemat Corso Duca Abruzzi 24 I-10129 Turin Italy 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (数学分析与应用杂志)

年 卷 期：2019年第471卷第1-2期

页      面：541-563页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：tau-Wigner distribution tau-Pseudodifferential operators Wiener amalgam spaces Modulation spaces 

摘      要：We study continuity properties on modulation spaces for tau-pseudodifferential operators Op(tau) (a) with symbols a in Wiener amalgam spaces. We obtain boundedness results for tau is an element of(0, 1) whereas, in the end-points tau = 0 and tau = 1, the corresponding operators are in general unbounded. Furthermore, for tau is an element of(0, 1), we exhibit a function of tau which is an upper bound for the operator norm. The continuity properties of Op(tau) (a), for any tau is an element of[0, 1], with symbols a in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on the parameter tau is an element of[0, 1], as expected. Key ingredients are uniform continuity estimates for tau-Wigner distributions. (C) 2018 Elsevier Inc. All rights reserved.