On the Hilbert-type operators acting from function spaces into sequence spaces

TL;DR

This paper investigates Hilbert-type operators that map functions into sequences, establishing conditions for their boundedness and compactness, and providing sharp norm estimates for specific cases.

Contribution

It introduces new Hilbert-type operators between function and sequence spaces and derives precise boundedness, compactness criteria, and norm estimates.

Findings

Established necessary and sufficient conditions for boundedness.

Derived criteria for compactness of the operators.

Obtained sharp norm estimates in special cases.

Abstract

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators. Also, for some special cases, we obtain the sharp estimates for the norms of certain Hilbert-type operators.