Maximal operator in Musielak--Orlicz--Sobolev spaces

Published 29 Mar 2023 in math.FA | (2303.16587v2)

Abstract: 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 $W^{{1,\varphi}(\mathbb{R}^n)$.}

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