The boundedness of Calderón-Zygmund operators by wavelet characterization

This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces H ^p(ℝ ⁿ). We use wavelet characterization of H ^p(ℝ ⁿ) to show that a Calderón-Zygmund operator T with T*1 = 0 is bounded on H ^p(ℝ ⁿ), n/n+ε < p ≤ 1, where ε 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.