Generalized riemann-stieltjes operators between hardy spaces and weighted bergman spaces

Abstract

Let m be a nonnegative integer and g ε H(B) such that g(0) = 0. We define a new integral-type operator, called the generalized Riemann-Stieltjes operator, as follows: L_g^(m) f(z) = ∫₀¹ R^mf(tz)g(tz)dt/t, z ε B. The boundedness of the generalized Riemann-Stieltjes operator between Hardy spaces and weighted Bergman spaces in the unit ball are investigated in this paper.