Musielak−Orlicz−Sobolev spaces on arbitrary metrique space

• Autorzy: Aissaoui N. , Akdim Y. , Hassib M. C.

Identyfikatory

DOI

10.14708/cm.v56i2.825

• Języki publikacji: EN

Abstrakty

EN

In this article we define Musielak−Orlicz−Sobolev spaces on arbitrary metric spaces with finite diameter and equipped with finite, positive Borel regular outer measure. We employ a Hajlasz definition, which uses a pointwise maximal inequality. We prove that these spaces are Banach, that the Poincaré inequality holds, and that the Lipschitz functions are dense. We develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. As an application, we prove that each Musielak−Orlicz−Sobolev function has a quasi-continuous representative.

Słowa kluczowe

EN

metric measure space; Musielak-Orlicz-Sobolev spaces; capacity

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 2
• Strony: 169--183
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Aissaoui N.

• Ecole Normale Superieure, B.P 5206, Ben Souda, Fez, Morocco

autor

Akdim Y.

• Faculty Poly-Disciplinary of Taza, Laboratory, LSI, Morocco

autor

Hassib M. C.

• SMBA University, Faculty of Science and Technique, Fez. Laboratory, LSI, Taza, Morocco

Bibliografia

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• [10] J. Kinnunen and O. Martio, The Sobolev capacity on metric spaces, Ann. Acad. Sci. Fenn. Math. 21 (1996), 367-382.
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• [12] J. Musielak, Orlicz Spaces and Modular Spaces, Berlin-Heidelberg 1983, DOI 10.1007/BFb0072210.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).