Integral operators on analytic Morrey spaces

Abstract

In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given

A family of Dirichlet–Morrey spaces

“…and act on functions f ∈ Hol(D). The operators I g , J g have been studied in a number of papers, see for example [1], [3], [7], [9] and [10]. Their relation to M g comes from the integration by parts formula…”

Embedding Theorems for Dirichlet Type Spaces

“…Aleman and Siskakis studied T g on H p and weighted Bergman spaces in [1,2]. Recently, the operators T g and I g between some spaces of analytic functions were investigated in [1,2,7,8,12,13,14,15,18,20,21,22] (see also the related references therein).…”

Volterra-type operators from analytic Morrey spaces to Bloch space

“…There are some articles about the integral operator acting on M orrey space. For example, Wu in [28] considered T g from Hardy to analytic M orrey spaces, Li, Liu and Lou [18] characterized the boundedness and essential norm of T g and I g on analytic M orrey spaces (see also the related references therein). Now, we need two spaces.…”