The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality

TL;DR

This paper extends the understanding of operator boundedness in Muckenhoupt weighted Morrey spaces by establishing duality and applying extrapolation techniques, resulting in new boundedness results even in unweighted scenarios.

Contribution

It generalizes the duality of Morrey spaces to weighted cases and combines it with extrapolation methods to derive new boundedness results for operators.

Findings

Duality of weighted Morrey spaces established

Boundedness of operators proven in new weighted contexts

Results applicable to unweighted Morrey spaces

Abstract

The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation techniques due to Rubio de Francia adapted to weighted Morrey spaces. This leads to new results on the boundedness of operators even for the unweighted case.