$L^p$ and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach

Claudia Garetto

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arXiv · 1011.1149

$L^p$ and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach

Claudia Garetto

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Abstract

In this paper we investigate $L^p$ and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net of mollifiers $(ρ_\eps)_\eps$, and we study the corresponding net of pseudodifferential operators providing $L^p$ and Sobolev estimates which relate the parameter $\eps$ with the non-regularity of the symbol.

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Claudia Garetto. 2010-11-04. $L^p$ and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach. https://arxiv.org/abs/1011.1149

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