Generalized Stević-Sharma type operators from derivative Hardy spaces into Zygmund-type spaces

Abstract

Let $ u, v $ be two analytic functions on the open unit disk $ {\mathbb D} $ in the complex plane, $ \varphi $ an analytic self-map of $ {\mathbb D} $, and $ m, n $ nonnegative integers such that $ m < n $. In this paper, we consider the generalized Stević-Sharma type operator $ T_{u, v, \varphi}^{m, n}f(z) = u(z)f^{(m)}(\varphi(z))+v(z)f^{(n)}(\varphi(z)) $ acting from the derivative Hardy spaces into Zygmund-type spaces, and investigate its boundedness, essential norm and compactness.

Keywords

• generalized stević-sharma operator
• derivative hardy space
• zygmund-type space
• essential norm