Abstract
We give sharp estimates for the fractional maximal function in terms of Hausdorff capacity. At the same time we identify the real interpolation spaces between L 1 and the Morrey space \(\mathcal{L}^{1,\lambda}\). The result can be viewed as an analogue of the Hardy–Littlewood maximal theorem for the fractional maximal function.
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Kruglyak, N., Kuznetsov, E. Sharp integral estimates for the fractional maximal function and interpolation. Ark Mat 44, 309–326 (2006). https://doi.org/10.1007/s11512-006-0019-4
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DOI: https://doi.org/10.1007/s11512-006-0019-4