BANACH ALGEBRA OF CALDERÓN-ZYGMUND OPERATORS ASSOCIATED TO PARA-ACCRETIVE FUNCTIONS

Abstract. In this paper, using the discrete Calderón-type reproducing formula as-sociated to para-accretive functions developed in [HLL], the authors prove that all Calderón-Zygmund operators satisfying T (b) = T ∗(b) = 0 form a Banach algebra, where b is a para-accretive function. This extends a result in [MC]. To generalize the Hilbert transform and Riesz transforms, Calderón and Zyg-mund developed a class of singular integral operators which are convolution op-erators. The L2-boundedness of such operators can be handled by Plancherel’s theorem. The Lp-boundedness, p 6 = 2, follows from the case p = 2 and from th