The continuity of pseudo-differential operators on weighted local Hardy spaces

Ming Yi Lee; Chin Cheng Lin; Ying Chieh Lin

doi:10.4064/sm198-1-4

The continuity of pseudo-differential operators on weighted local Hardy spaces

Ming Yi Lee, Chin Cheng Lin, Ying Chieh Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We first show that a linear operator which is bounded on L², with ε A₁ can be extended to a bounded operator on the weighted local Hardy space h₁, if and only if this operator is uniformly bounded on all h₁-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to h ¹.

Original language	English
Pages (from-to)	69-77
Number of pages	9
Journal	Studia Mathematica
Volume	198
Issue number	1
DOIs	https://doi.org/10.4064/sm198-1-4
State	Published - 2010

Keywords

Pseudo-differential operators
Weighted local hardy spaces

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10.4064/sm198-1-4

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AB - We first show that a linear operator which is bounded on L2, with ε A1 can be extended to a bounded operator on the weighted local Hardy space h1, if and only if this operator is uniformly bounded on all h1-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to h 1.

KW - Pseudo-differential operators

KW - Weighted local hardy spaces

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JO - Studia Mathematica

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The continuity of pseudo-differential operators on weighted local Hardy spaces

Abstract

Keywords

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