Maximal operator in Musielak--Orlicz--Sobolev spaces (2303.16587v2)

Published 29 Mar 2023 in math.FA

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