The boundedness of Calderón-Zygmund operators by wavelet characterization

Abstract

This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces H p(ℝn). We use wavelet characterization of H p(ℝn) to show that a Calderón-Zygmund operator T with T*1 = 0 is bounded on H p(ℝn), \(\tfrac{n} {{n + \varepsilon }} < p \leqslant 1\) is the regular exponent of kernel of T. This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.