Weighted Lp-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Kazumasa Fujiwara; Tohru Ozawa

doi:10.2969/jmsj/06810169

Weighted Lp-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Kazumasa Fujiwara, Tohru Ozawa

School of Advanced Science and Engineering

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

Abstract

We study the boundedness of integral operators of convolution type in the Lebesgue spaces with weights. As a byproduct, we give a simple proof of the fact that the standard Sobolev space H^s(Rⁿ) forms an algebra for s > n/2. Moreover, an optimality criterion is presented in the framework of weighted Lp-boundedness.

Original language	English
Pages (from-to)	169-191
Number of pages	23
Journal	Journal of the Mathematical Society of Japan
Volume	68
Issue number	1
DOIs	https://doi.org/10.2969/jmsj/06810169
Publication status	Published - 2016

Keywords

Pointwise multiplication
Sobolev spaces

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06810169

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abstract = "We study the boundedness of integral operators of convolution type in the Lebesgue spaces with weights. As a byproduct, we give a simple proof of the fact that the standard Sobolev space Hs(Rn) forms an algebra for s > n/2. Moreover, an optimality criterion is presented in the framework of weighted Lp-boundedness.",

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KW - Sobolev spaces

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Weighted Lp-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Abstract

Keywords

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