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.
Citation
Xing Fu. Dachun Yang. Wen Yuan. "GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES." Taiwanese J. Math. 18 (2) 509 - 557, 2014. https://doi.org/10.11650/tjm.18.2014.3651
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