Generalized integration operators on Hardy spaces

Abstract: Inspired by the study of generalized Cesaro operator T_g introduced by Aleman and Siskakis we study a variation of this operator,namely P(g,a) , depending on an analytic symbol g and an n - tuple of complex numbers, a . Regarding the boundedness properties of this operator we prove that P(g,a) is a bounded linear operator from H^p to itself if and only if g is an analytic function of bounded mean oscillation and compact if and only if g is of vanishing mean oscillation. Furthermore in the special case n=2, a=0 we completely characterized the functions g for which P(g,a) is bounded from H^p to H^q, 0