Pseudo-Differential Operators on Sobolev and Lipschitz Spaces

In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2010, Vol.26 (1), p.131-142
Main Authors: Lin, Yan, Lu, Shan Zhen
Format: Article
Language:English
Subjects:
Fourier transforms
Hypotheses
Lipschitz空间
Mathematics
Mathematics and Statistics
Sobolev空间
Studies
交换子
伪微分算子
勒贝格
有界性
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Summary:In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-010-8109-4