Formula omitted] and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach

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 ε ) ε , and we study the corresponding net of pseudodifferential operators providing L p and Sobolev estimates which relate the parameter ε with the non-regularity of the symbol.