Extended Cesàro operators on Bergman spaces

Abstract

We define an extended Cesàro operator T g with holomorphic symbol g in the unit ball B of C n . For a large class of weights w we characterize those g for which T g is bounded (or compact) from Bergman space L p a,w (B) to L q a,w (B), 0 < p, q < ∞. In addition, we obtain some results about equivalent norms, the norm of point evaluation functionals, and the interpolation sequences on L p a,w (B).

Riemann-Stieltjes operators from F(p,q,s) spaces to α-Bloch spaces on the unit ball

“…It was introduced in [5], and studied in [5-7, 15, 17]. Here, we extend operator I g for the case of holomorphic functions on the unit ball as follows:…”

On an integral operator on the unit ball in

“…This operator can be considered as a natural extension of operator (1.6) on H(B) (when n = 1 we indeed obtain (1.6)). Operator (1.13) has appeared, for the first time, in [6] where its boundedness and compactness are investigated.…”

Fractional derivatives of pointwise multipliers between holomorphic spaces

“…These operators have been thoroughly studied in different settings, and there is a wide literature on the subject. See for instance the classical articles [5], [4] and [20], the recent paper [26] and the references therein. We study the relationship of these operators with the multipliers, extending some classical results on this topic.…”