Journal of the Mathematical Society of Japan

Weighted $L^p$-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Kazumasa FUJIWARA and Tohru OZAWA

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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 $H^s(\mathbb{R}^n)$ forms an algebra for $s$ > $n/2$. Moreover, an optimality criterion is presented in the framework of weighted $L^p$-boundedness.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 1 (2016), 169-191.

Dates
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1453731540

Digital Object Identifier
doi:10.2969/jmsj/06810169

Mathematical Reviews number (MathSciNet)
MR3454558

Zentralblatt MATH identifier
1342.26043

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 42B

Keywords
pointwise multiplication Sobolev spaces

Citation

FUJIWARA, Kazumasa; OZAWA, Tohru. Weighted $L^p$-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces. J. Math. Soc. Japan 68 (2016), no. 1, 169--191. doi:10.2969/jmsj/06810169. https://projecteuclid.org/euclid.jmsj/1453731540


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