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

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 $W^{k,1}$. As applications, some bounded and unbounded properties of Hardy operator and adjoint Hardy operator on $W^{k,1}$ are deduced.

References in corpus (1)

• Hausdorff operators on modulation and Wiener amalgam spaces