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Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator

Sundaram Thangavelu and Venku Naidu Dogga

Abstract

This article deals with Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator G:=-Δ-|x|22t2 on n+1. We make use of the Lp boundedness of Riesz transforms for the Grushin operator in studying the wave equation.

MSC 2010: 42C10; 46E30; 47D09

Funding statement: The work of the first author is supported by J. C. Bose National Fellowship from the Department of Science and Technology (DST), India. The work of the second author is supported by the Department of Science and Technology (DST), India and Indian Institute of Technology Hyderabad, India.

References

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Received: 2017-4-16
Revised: 2017-7-5
Accepted: 2017-7-6
Published Online: 2017-8-8
Published in Print: 2018-4-1

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