MORREY MEETS MUCKENHOUPT: A NOTE ON NAKAI'S GENERALIZED MORREY SPACES AND APPLICATIONS

Xue Zhao; Xianming Hou; Qingyan Wu; Zunwei Fu

doi:10.11948/20240481

2025 Volume 15 Issue 5

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Xue Zhao, Xianming Hou, Qingyan Wu, Zunwei Fu. MORREY MEETS MUCKENHOUPT: A NOTE ON NAKAI'S GENERALIZED MORREY SPACES AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2884-2899. doi: 10.11948/20240481

Citation:

Xue Zhao, Xianming Hou, Qingyan Wu, Zunwei Fu. MORREY MEETS MUCKENHOUPT: A NOTE ON NAKAI'S GENERALIZED MORREY SPACES AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2884-2899. doi: 10.11948/20240481

MORREY MEETS MUCKENHOUPT: A NOTE ON NAKAI'S GENERALIZED MORREY SPACES AND APPLICATIONS

1.
School of Mathematics and Statistics, Linyi University, Linyi 276005, China

Author Bio: Email: zhaoxue202309@163.com(X. Zhao); Email: wuqingyan@lyu.edu.cn(Q. Wu); Email: fuzunwei@lyu.edu.cn(Z. Fu)
Corresponding author: Email: houxianming37@l63.com(X. Hou)
Fund Project: This work was supported by the National Natural Science Foundation of China (Nos. 12301118, 12071197, 12171221, 12271232) and the Natural Science Foundation of Shandong Province (Nos. ZR2021MA031, ZR2021MA079)

Abstract

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.
- Morrey space /
- one-sided weight /
- sublinear operator /
- fractional integral /
- fractional differential equation
MSC: 42B35, 42B20, 26A33

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References

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