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 \cite{LLY} (J. Math. Anal. Appl. 301 (2005), 394--400) established that
the Riesz transforms Rj​,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 \cite{LLY}, consists in passing
from atoms to all functions in Hwp​(Rn). Furthermore, the
Hwp​-boundedness of θ-Calder\'on-Zygmund operators are also given
through molecular characterization and atomic decomposition.Comment: to appear in Anal. Theory. Appl. 27 (2011), no. 3, 251-26