Boundedness of fractional integral operators on non-homogeneous metric measure spaces

2013/08/26 by Rulong Xie, Xie, Rulong, Shu, Lisheng
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1308.5483

openalex publication_date 2013/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with fractional kernel of order α and regularity ε introduced by García-Cuerva and Gatto as special cases. And the (L^p(μ),L^q(μ))-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the (L^p(μ),L^q(μ))-boundedness for commutators and multilinear commutators generated by fractional integral operators with RBMO(μ) function are further obtained. These results in this paper includes the corresponding results on both the homogeneous spaces and non-doubling measure spaces.

Citations

• Spaces of Type BLO on Non-homogeneous Metric Measure Spaces

Related

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• Boundedness properties of fractional integral operators associated to non--doubling measures
• Multilinear Fractional Integral Operators with Generalized Kernels
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