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On weighted $ L^2$ estimates for solutions of the wave equation


Authors: Youngwoo Koh and Ihyeok Seo
Journal: Proc. Amer. Math. Soc. 144 (2016), 3047-3061
MSC (2010): Primary 35B45; Secondary 35L05, 42B35
DOI: https://doi.org/10.1090/proc/12951
Published electronically: January 27, 2016
MathSciNet review: 3487235
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Abstract: In this paper we consider weighted $ L^2$ integrability for solutions of the wave equation. For this, we obtain some weighed $ L^2$ 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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Additional Information

Youngwoo Koh
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
Email: ywkoh@kias.re.kr

Ihyeok Seo
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
Email: ihseo@skku.edu

DOI: https://doi.org/10.1090/proc/12951
Keywords: Weighted estimates, wave equation, Morrey-Campanato class
Received by editor(s): January 9, 2015
Received by editor(s) in revised form: September 4, 2015
Published electronically: January 27, 2016
Additional Notes: The first author was supported by NRF grant 2012-008373.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society