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arXiv · 2608.17918

Properties and applications of Lorentz--Muckenhoupt classes

Dinghuai Wang·Qian Zhang
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Abstract

In this paper, through the introduction of Lorentz--Muckenhoupt classes, we systematically investigate the boundedness of maximal operators on multiplier weighted Lorentz spaces. As applications, we give the characterization of the commutators of fractional integrals, which yields a partial answer to an open question proposed by D. Cruz-Uribe. Second, Hardy inequalities in Lorentz spaces are established, with the critical case $p=d$, in which the classical Hardy inequality fails. Finally, we apply the Lorentz estimates to fractional Schr\"odinger equations with singular potentials.

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Dinghuai Wang, Qian Zhang. 2026-08-18. Properties and applications of Lorentz--Muckenhoupt classes. https://arxiv.org/abs/2608.17918

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