Discrete Riesz Potentials on Discrete Weighted Morrey Spaces

2023/10/12 by Xuebing Hao, Shuai Yang, Hao, Xuebing +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2310.08458

Abstract

Let 0<α<1. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators \mathcal M_α on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we deduce the boundedness of the discrete Riesz potentials I_α on discrete weighted Lebesgue spaces. The boundedness of I_α on discrete weighted Morrey spaces is further obtained. Moreover, the boundedness of \mathcal M_α is also obtained which is new even for unweighted case.

Related

• The Hardy-Littlewood Maximal Operator on Discrete Morrey Spaces
• Classical discrete operators on variable ℓ^p(⋅)(ℤ) spaces
• The Hardy-Littlewood Maximal Operator on Discrete Weighted Morrey Spaces
• Endpoint estimates of discrete fractional operators on discrete weighted Lebesgue spaces
• Boundedness of the Hardy-Littlewood Maximal Operator, Fractional Integral Operators, and Calderon-Zygmund Operators on Generalized Weighted Morrey Spaces