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

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

2010-11-04

arxiv.org/abs/1011.1149v1

Mathematics

Analysis of PDEs

Scientific paper

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 $(\rho_\eps)_\eps$, 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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