Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces

Abstract In this article, we establish a new atomic decomposition for , where the decomposition converges in -norm rather than in the distribution sense. As applications of this decomposition, assuming that T is a linear operator bounded on and 0 < p ≤ 1, we obtain (i) if T is uniformly bounded in -norm for all w-p-atoms, then T can be extended to be bounded from to ; (ii) if T is uniformly bounded in -norm for all w-p-atoms, then T can be extended to be bounded on ; (iii) if T is bounded on , then T can be extended to be bounded from to .