Taiwanese Journal of Mathematics

GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES

Xing Fu, Dachun Yang, and Wen Yuan

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Abstract

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional integrals over $({\mathcal X},d,\mu)$. The authors also prove that multilinear commutators of fractional integrals with RBMO(μ) functions are bounded on Orlicz spaces over $({\mathcal X},d,\mu)$, which include Lebesgue spaces as special cases. The weak type endpoint estimates for multilinear commutators of fractional integrals with functions in the Orlicz-type space ${\mathrm{Osc}_{\exp L^r}(\mu)}$, where $r\in [1,\infty)$, are also presented. Finally, all these results are applied to a specific example of fractional integrals over non-homogeneous metric measure spaces.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 509-557.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706401

Digital Object Identifier
doi:10.11650/tjm.18.2014.3651

Mathematical Reviews number (MathSciNet)
MR3188518

Zentralblatt MATH identifier
1357.42016

Subjects
Primary: 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s- numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Secondary: 47B47: Commutators, derivations, elementary operators, etc.

Keywords
non-homogeneous metric measure space fractional integral commutator Orlicz space Hardy space RBMO(μ) ${\mathrm{Osc}_{\exp L^r}(\mu)}$

Citation

Fu, Xing; Yang, Dachun; Yuan, Wen. GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES. Taiwanese J. Math. 18 (2014), no. 2, 509--557. doi:10.11650/tjm.18.2014.3651. https://projecteuclid.org/euclid.twjm/1499706401


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