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arXiv · 1710.10603

Hausdorff operators on the Sobolev spaces $W^{k,1}$

Guoping Zhao·Weichao Guo
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Abstract

This paper is served as a first contribution regarding the boundedness of Hausdorff operators on function spaces with smoothness. The sharp conditions are established for boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$. As applications, some bounded and unbounded properties of Hardy operator and adjoint Hardy operator on $W^{k,1}$ are deduced.

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Guoping Zhao, Weichao Guo. 2017-10-29. Hausdorff operators on the Sobolev spaces $W^{k,1}$. https://arxiv.org/abs/1710.10603

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