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

Abstract: In this paper we investigate 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 , and we study the corresponding net of pseudodifferential operators providing and Sobolev estimates which relate the parameter ε with the non-regularity of the symbol. [Copyright &y& Elsevier]