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TBDmathscidoc:1701.333084

Arkiv for Matematik, 44, (2), 309-326, 2005.5
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.
@inproceedings{natan2005sharp,
title={Sharp integral estimates for the fractional maximal function and interpolation},
author={Natan Kruglyak, and Evgeny A. Kuznetsov},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617409756893},
booktitle={Arkiv for Matematik},
volume={44},
number={2},
pages={309-326},
year={2005},
}

Natan Kruglyak, and Evgeny A. Kuznetsov. Sharp integral estimates for the fractional maximal function and interpolation. 2005. Vol. 44. In Arkiv for Matematik. pp.309-326. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617409756893.