A class of bounded pseudo-differential operators

Pseudo-differential operators of order -M and type rho, delta(1), delta(2) are shown to be bounded in L(2) provided that 0 </= rho </= delta(1) < 1, 0 </= rho </= delta(2) < 1, and [Formula: see text].

Cauchy integrals on Lipschitz curves and related operators

In this note, we establish certain properties of the Cauchy integral on Lipschitz curves and prove the L(p)-boundedness of some related operators. In particular, we obtain the recent results of R. R. Coifman and Y. Meyer [(1976) "Commutateurs d'intégrales singulières:" Analyse harmonique d'Orsay n(o) 211, Université Paris XI] on the continuity of the so-called commutator operators.