Square-like Functions Generated by a Composite Wavelet Transform

Abstract

The classical square functions play important role in Harmonic Analysis and have a very direct connection with L2-estimates and Littlewood-Paley theory. In this paper we introduce a new variant of square-like functions generated by some composite wavelet transform. We establish Calderón-type reproducing formula and then prove L2-boundedness of newly defined square-like functions.Mathematics Subject Classification (2010). Primary 42C40; Secondary 44A35, 26D15.