Piotr Michał Bies

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math.FA2023

Maximal operator in Musielak--Orlicz--Sobolev spaces

Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka

We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1, φ} (R^{n})$ . Under some natural assumptions on $φ$ we show that the maximal function…

math.FA2023

Maximal operator in Hölder spaces

Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka

We study the maximal operator on the variable exponent Hölder spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annu…