Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka
Published 2023-03-29Version 1
We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1,\varphi}(\mathbb{R}^n)$. Under some natural assumptions on $\varphi$ we show that the maximal function is bounded and continuous in $W^{1,\varphi}(\mathbb{R}^n)$.
Maximal inequalities for dual Sobolev spaces $W^{-1,p}$ and applications to interpolation
On a discrete version of Tanaka's theorem for maximal functions
The Muckenhoupt condition
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