Closed range of generalized integration operators on analytic tent spaces

TL;DR

This paper characterizes when the generalized integration operator $T_g^{n,k}$ has a closed range on analytic tent spaces, providing necessary and sufficient conditions for this property.

Contribution

It establishes the exact conditions under which the generalized integration operator has a closed range on analytic tent spaces, advancing the understanding of operator behavior in these spaces.

Findings

Derived necessary and sufficient conditions for closed range of $T_g^{n,k}$.

Enhanced understanding of operator properties on analytic tent spaces.

Contributed to the theory of generalized integration operators.

Abstract

In this paper, the necessary and sufficient conditions for the generalized integration operator $T_g^{n,k}$ to have closed ranges on the analytic tent spaces are investigated.