Abstract. In this article we give some sufficient conditions for the boundedness and compactness of a weighted composition operator on the Hardy spaces $H^p$, $1\leq p< \infty $, in terms of an appropriate weighted counting function and a Volterra type integral operator.

AMS Subject Classification (1991): 47B33, 47B38; 46E15

Keyword(s): weighted composition operators, counting function

Received April 20, 2011, and in revised form May 11, 2011. (Registered under 21/2011.)