Schr\"odinger type operators on generalized Morrey spaces

TL;DR

This paper introduces generalized Morrey spaces linked to Schr"odinger operators and proves the boundedness of certain related operators on these spaces, expanding the understanding of Schr"odinger operator behavior in function spaces.

Contribution

It defines a new class of generalized Morrey spaces associated with Schr"odinger operators and establishes boundedness results for specific operators on these spaces.

Findings

Boundedness of $V^{eta_{2}}(- riangle+V)^{-eta_{1}}$ on generalized Morrey spaces

Pointwise estimates used to prove operator boundedness

Extension of Morrey space theory to Schr"odinger operators

Abstract

In this paper we introduce a class of generalized Morrey spaces associated with Schr\"odinger operator $L=-\Delta+V$. Via a pointwise estimate, we obtain the boundedness of the operators $V^{\beta_{2}}(-\Delta+V)^{-\beta_{1}}$ and their dual operators on these Morrey spaces.