AN INTEGRAL TYPE OPERATOR ON $S^p$ SPACES AND ITS ESSENTIAL NORM

Year 2025, Volume: 15 Issue: 9, 2229 - 2238, 01.09.2025

Mina Safarzadeh Mostafa Hassanlou , Mina Ettefagh Zohreh Zeinalabedini Charandabi

Abstract

Given two analytic functions $\lambda: \mathbf{D} \rightarrow \mathbf{D}$ and $\nu: \mathbf{D} \rightarrow \mathbb{C}$ and $n \in \mathbb{N}_0$, we study boundedness of the integral-type operator $C_{\lambda,\nu}^n$ acting from derivative Hardy space into Zygmund space. We also get an approximation for the essential norm of this operator. A characterization for compactness of the operator can be obtained from the essential norm.

Keywords

Hardy space. , Integral-type operator , Essential norm , Zygmund type space

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