The boundedness of some operators with rough kernel on the weighted Morrey spaces

2010/11/26 by Hua Wang, Wang, Hua
Mathematics · #42B20 #42B25 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CA #msc:42B20 #msc:42B25 #msc:42B35

paper · pdf · doi:10.48550/arxiv.1011.5763

17 pages

arxiv created 2010/11/26 · openalex publication_date 2010/11/26 · arxiv updated 2010/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω∈ L^q(S^n-1) with 1<q≤∞ be homogeneous of degree zero and has mean value zero on S^n-1. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces L^p,κ(w) for q'≤ p<∞(or q'<p<∞) and 0<κ<1. We will also prove that the commutator operators formed by a BMO(\mathbb Rⁿ) function b(x) and these rough operators are bounded on the weighted Morrey spaces L^p,κ(w) for q'<p<∞ and 0<κ<1.

Citations

• On functions of bounded mean oscillation
• On the solutions of quasi-linear elliptic partial differential equations

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