Weighted conditional type operators between different Orlicz spaces

TL;DR

This paper investigates the boundedness and norm estimates of weighted conditional type operators between different Orlicz and L^p spaces, providing necessary and sufficient conditions and bounds for these operators.

Contribution

It introduces new criteria for the boundedness of weighted conditional type operators between various Orlicz spaces and L^p spaces, extending previous results.

Findings

Characterization of boundedness conditions for weighted conditional type operators

Necessary and sufficient conditions for boundedness between different Orlicz and L^p spaces

Upper and lower bounds for the essential norm of these operators

Abstract

In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of weighted conditional type operators. As a consequence we characterize boundedness of weighted conditional type operators and multiplication operators between different L^p-spaces. Finally, we give some upper and lower bounds for essential norm of weighted conditional type operators.