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Sharp integral estimates for the fractional maximal function and interpolation

Natan Kruglyak Department of Mathematics, Luleå University of Technology Evgeny A. Kuznetsov Department of Mathematics, Luleå University of Technology

TBD mathscidoc: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.
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@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.
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