Two type Estimates for the Boundedness of Generalized Riesz Potential Operator in the Generalized Weighted Local Morrey Spaces

TL;DR

This paper establishes boundedness properties of the generalized Riesz potential operator across various generalized weighted local Morrey spaces, extending classical results to more general settings.

Contribution

It introduces two types of boundedness estimates for the operator, broadening the understanding of its behavior in weighted Morrey space frameworks.

Findings

Proves Spanne-type boundedness between generalized weighted local Morrey spaces.

Establishes Adams-type boundedness from weighted spaces to other spaces.

Demonstrates boundedness to weak spaces, enhancing operator theory in function spaces.

Abstract

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator from the one generalized weighted local Morrey spaces to the another one, and from the generalized weighted local Morrey spaces to the weak generalized weighted local Morrey spaces. We also prove the Adams-type boundedness of the operator from the weighted spaces to the another one, and from the weighted spaces to the weak weighted spaces.