2010•arXiv (Cornell University)Open access
$L^p$ and Sobolev boundedness of pseudodifferential operators with\n 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\nof pseudodifferential operators with non-regular symbols. We employ\nregularisation methods, namely convolution with a net of mollifiers\n$(\\rho_\\eps)_\\eps$, and we study the corresponding net of pseudodifferential\noperators providing $L^p$ and Sobolev estimates which relate the parameter\n$\\eps$ with the non-regularity of the symbol.\n
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