On weighted L2 estimates for solutions of the wave equation

Youngwoo Koh; Ihyeok Seo

doi:10.1090/proc/12951

On weighted L² estimates for solutions of the wave equation

Youngwoo Koh, Ihyeok Seo

Department of Mathematics

Korea Institute for Advanced Study

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

4 Scopus citations

Abstract

In this paper we consider weighted L² integrability for solutions of the wave equation. For this, we obtain some weighed L² estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and a localization argument which makes use of the Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.

Original language	English
Pages (from-to)	3047-3061
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	7
DOIs	https://doi.org/10.1090/proc/12951
State	Published - Jul 2016

Keywords

Morrey-Campanato
Wave equation
Weighted estimates

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10.1090/proc/12951

Cite this

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abstract = "In this paper we consider weighted L2 integrability for solutions of the wave equation. For this, we obtain some weighed L2 estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and a localization argument which makes use of the Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.",

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AB - In this paper we consider weighted L2 integrability for solutions of the wave equation. For this, we obtain some weighed L2 estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and a localization argument which makes use of the Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.

KW - Morrey-Campanato

KW - Wave equation

KW - Weighted estimates

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DO - 10.1090/proc/12951

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EP - 3061

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

On weighted L² estimates for solutions of the wave equation

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Keywords

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