摘要
Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp （Rn）. 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 HwP（Rn）. Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.
Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp （Rn）. 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 HwP（Rn）. Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.
