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SOME SHARP BILINEAR SPACE–TIME ESTIMATES FOR THE WAVE EQUATION

Part of: Harmonic analysis in several variables Hyperbolic equations and systems Partial differential equations

Published online by Cambridge University Press:  07 March 2016

Neal Bez ,
Chris Jeavons  and
Tohru Ozawa
Neal Bez
Affiliation:
Department of Mathematics, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan email nealbez@mail.saitama-u.ac.jp
Chris Jeavons
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K. email jeavonsc@maths.bham.ac.uk
Tohru Ozawa
Affiliation:
Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan email txozawa@waseda.jp

Abstract

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We prove a family of sharp bilinear space–time estimates for the half-wave propagator $\text{e}^{\text{i}t\sqrt{-\unicode[STIX]{x1D6E5}}}$ . As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.

MSC classification

Primary: 35B45: A priori estimates
Secondary: 35L05: Wave equation 42B37: Harmonic analysis and PDE

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 719 - 737
Copyright
Copyright © University College London 2016 

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