Sharp conditions for the compactness of the Sobolev embedding on Musielak–Orlicz spaces
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DOI: 10.1002/mana.201700462
Abstract: We prove the compactness of the Sobolev embedding for Musielak–Orlicz spaces by way of simple conditions on the Matuszewska index of the underlying space. We provide counterexamples to show the sharpness of our conditions. read more here.
Keywords: sharp conditions; embedding musielak; sobolev embedding; compactness sobolev ... See more keywords
Gossez's approximation theorems in Musielak–Orlicz–Sobolev spaces
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DOI: 10.1016/j.jfa.2018.05.015
Abstract: We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity assumption on $M$… read more here.
Keywords: orlicz sobolev; gossez approximation; musielak orlicz; sobolev spaces ... See more keywords
Atomic characterizations of weak martingale Musielak–Orlicz Hardy spaces and their applications
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DOI: 10.1215/17358787-2018-0050
Abstract: Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $\varphi:\ \Omega\times[0,\infty)\to [0,\infty)$ be a Musielak--Orlicz function. In this article, the authors establish the atomic characterizations of weak martingale Musielak--Orlicz Hardy spaces $WH_{\varphi}^s(\Omega)$, $WH_{\varphi}^M(\Omega)$, $WH_{\varphi}^S(\Omega)$, $WP_{\varphi}(\Omega)$ and $WQ_{\varphi}(\Omega)$.… read more here.
Keywords: varphi omega; musielak orlicz; orlicz hardy; hardy spaces ... See more keywords
Upper Local Uniform Monotonicity in F-Normed Musielak–Orlicz Spaces
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DOI: 10.3390/axioms12060539
Abstract: In this paper, the necessary and sufficient conditions for the upper strict monotonicity point and the upper local uniform monotonicity point are given in the case of Musielak–Orlicz spaces equipped with the Mazur–Orlicz F-norm. Moreover,… read more here.
Keywords: monotonicity; upper local; musielak orlicz; local uniform ... See more keywords