Hausdorff operators on the Sobolev spaces Wk,1
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 Wk,1. As applications, some bounded and unbounded properties of Hardy operator and adjoint Hardy operator on Wk,1 are deduced.
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