A NOTE ON H~-_w-BOUNDEDNESS OF RIESZ TRANSFORMS AND θ-CALDERON-ZYGMUND OPERATORS THROUGH MOLECULAR CHARACTERIZATION

摘要

Let θ < p < 1 and w in the Muckenhoupt class A. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and Yang established that the Riesz transforms Rj, j = 1,2, ... n, are bounded on H ~ p_w(R~n). In this note we extend this to the general case of weight w in the Muckenhoupt class A,*, through molecular characterization. One difficulty, which has not been taken care in [11], consists in passing from atoms to all functions in H~ p_w(R"). Furthermore, the H~p_w-boundedness of θ-Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.