  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
$(\rho_\eps)_\eps$, and we study the corresponding net of pseudodifferential
operators providing $L^p$ and Sobolev estimates which relate the parameter
$\eps$ with the non-regularity of the symbol.
