The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs

Rainer Mandel

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arXiv · 2303.03020

The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs

Rainer Mandel

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Abstract

We prove $L^p$-$L^q$-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. Similar techniques apply to the Limiting Absorption Principles for certain elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on $\mathbb{R}^d$ with block-radial right hand sides.

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Rainer Mandel. 2023-03-06. The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs. https://arxiv.org/abs/2303.03020

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