Pseudo-differential operators of class \(S^m_{0,0}\) on the Herz-type spaces (Q1029967)
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scientific article; zbMATH DE number 5578125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudo-differential operators of class \(S^m_{0,0}\) on the Herz-type spaces |
scientific article; zbMATH DE number 5578125 |
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Pseudo-differential operators of class \(S^m_{0,0}\) on the Herz-type spaces (English)
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14 July 2009
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The author studies the action of pseudo-differential operators with symbol in the classes \(S^m_{0,0}\) on Herz-type spaces [cf.\ \textit{C.\,S. Herz}, J.~Math.\ Mech.\ 18, 283--323 (1968; Zbl 0177.15701)]. Boundedness is obtained for suitable orders \(m< 0\). The proof is based on arguments of atomic decomposition and analytic interpolation theory [cf.\ \textit{A.\,Miyachi}, Math.\ Nachr.\ 133, 135- -154 (1987; Zbl 0638.35089); \textit{A.\,Tabacco Vignati}, Indiana Univ.\ Math.\ J.\ 37, No.\,1, 1--21 (1988; Zbl 0628.46071)].
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pseudodifferential operators
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Herz-type spaces
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interpolation of quasi-Banach spaces
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0.91955036
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0.91051763
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0.9064477
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0.9048211
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0.9013148
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0.89980024
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