Hausdorff operators on the Sobolev spaces $W^{k,1}$
Guoping Zhao, Weichao Guo
TL;DR
This paper establishes sharp conditions for the boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$, advancing understanding of their behavior on smooth function spaces and analyzing related Hardy operators.
Contribution
It provides the first comprehensive criteria for the boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$ and explores applications to Hardy operators.
Findings
Sharp boundedness conditions for Hausdorff operators on $W^{k,1}$
Boundedness and unboundedness properties of Hardy operators on $W^{k,1}$
New insights into operator behavior on smooth function spaces
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 . As applications, some bounded and unbounded properties of Hardy operator and adjoint Hardy operator on are deduced.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems