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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 . Under some natural assumptions on 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…
math.AP2023
Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity
Piotr Michał Bies, Tomasz Cieślak
We construct unique regular solutions to the minimal nonlinear system of the 1d thermoelasticity. The obtained solution has a positive temperature. Our approach is based on an esti…