Compactness of Riemann-Stieltjes operators between F(p,q,s) spaces and α-Bloch spaces

Abstract

Let H(B) denote the space of all holomorphic functions on the unit ball B ⊂ ℂ n. In this paper we investigate the following integral operators T g(f)(z) = ∫ 01 f(tz)ℜg(tz)dt/t and L g(f)(z) = ∫ 01 Rf(tz)g(tz) dt/t, f ∈ H(B), z ∈ B, where g ∈ H(B) and ℜh(z) = Σ j=1n z j∂h/∂z j(z) is the radial derivative of h. The operator T g can be considered as an extension of the Cesàro operator on the unit disk. The compactness of the operators T g and L g between the general function space F(p, q, s), which includes the Hardy space, Bergman space, Bloch space, and Q p space, and the α-Bloch space are discussed.