Fractional maximal operators map BMO functions into Hausdorff-content BLO spaces, send BMO to VMO via uniform continuity, and preserve vanishing mean oscillation spaces adapted to dyadic Hausdorff content.
On Hausdorff content maximal operator and Riesz potential for non-measurable functions
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abstract
We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or extended now using integrals taken in the sense of Choquet with respect to Hausdorff content. Some earlier results also for maximal operators are considered, but now for non-measurable functions.
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Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content
Fractional maximal operators map BMO functions into Hausdorff-content BLO spaces, send BMO to VMO via uniform continuity, and preserve vanishing mean oscillation spaces adapted to dyadic Hausdorff content.