Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach

In this paper we investigate Lp 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 (ρε)ε, and we study the corresponding net of pseudodifferential operators providing Lp and Sobolev estimates which relate the parameter ε with the non-regularity of the symbol.