Maximal and fractional maximal operators in the Lorentz Morrey spaces and their applications to the Bochner Riesz and Schrodinger type operators

TL;DR

This paper establishes boundedness conditions for maximal and fractional maximal operators in Lorentz Morrey spaces and applies these results to analyze the boundedness of Bochner Riesz and Schrödinger operators with potentials in reverse Hölder classes.

Contribution

It introduces new boundedness criteria for fractional maximal operators in Lorentz Morrey spaces and applies these to important integral operators in harmonic analysis.

Findings

Derived sharp rearrangement estimates for maximal functions.

Established necessary and sufficient conditions for fractional maximal operators.

Proved boundedness of Bochner Riesz and Schrödinger operators in Lorentz Morrey spaces.

Abstract

The aim of this paper is to obtain boundedness conditions for the maximal function Mf and to prove the necessary and sufficient conditions for the fractional maximal oparator Ma in the Lorentz Morrey spaces which are a new class of functions. We get our main results by using the obtained sharp rearrangement estimates. The obtained results are applied to the boundedness of particular operators such as the Bochner Riesz operator and the Schrodinger type operators in the Lorentz Morrey spaces, where the nonnegative potential V belongs to the reverse Holder class.