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

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 (sigma(epsilon))(epsilon), and we study the corresponding net of pseudodifferential operators providing L-p and Sobolev estimates which relate the parameter epsilon with the non-regularity of the symbol. (C) 2011 Elsevier Inc. All rights reserved.