Work

Morrey Meets Muckenhoupt: a Note on Nakai's Generalized Morrey Spaces and Applications

Year: 2025

Type: article

Abstract: In this paper, we introduce the generalized one-sided weighted Morrey spaces, which extend Nakai's generalized Morrey spaces to a wider function class, the one-sided Muckenhoupt weighted case. Morrey matching Muckenhoupt enables us to study both the weak and strong type boundedness of one-sided sublinear operators under certain size conditions. Moreover, we establish the boundedness of the Riemann-Liouville fractional integral and the compactness of the truncated Riemann-Liouville integral on these spaces. As an application, we obtain the existence and uniqueness of solutions to a Cauchy-type problem for fractional differential equations.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240481

Authors: Xue Zhao, Xianming Hou, Qingyan Wu, Zunwei Fu

Institution: Linyi University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province