Calderón–Zygmund Operators on Weighted Hardy Spaces

Abstract

We study the boundedness of Calderon–Zygmund operators on weighted Hardy spaces \(H^p_w\) using Littlewood-Paley theory. It is shown that if a Calderon–Zygmund operator T satisfies T *1 = 0, then T is bounded on \(H^p_w\) for \(w\in A_{p(1+\frac\varepsilon n)}\) and \(\frac n{n+\varepsilon}<p\le1\), where e is the regular exponent of the kernel of T.