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

By Xing Fu, Dachun Yang, Wen Yuan. 2013

67 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/eb094d0d34f7d35bfcfd1ebbc0b9e29ac31739d5

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1. T. Nogayama
2. Long Huang
3. Dachun Yang

Citations in the corpus

• Boundedness of commutators of fractional integral operators on mixed Morrey spaces (2019, methodology): “Usually, when we handle commutators, the sharp maximal operator is a useful tool as was done in [22,31,33].”