This article is cited in 3 papers

Sobolev embedding theorems and generalizations for functions on a metric measure space

N. N. Romanovskiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Considering the metric case, we define an analog of the Sobolev space of functions with generalized derivatives of order greater than 1. The space of functions with fractional generalized derivatives is also treated. We prove generalizations of the Sobolev embedding theorems and Gagliardo–Nirenberg interpolation inequalities to the metric case.

Keywords: Sobolev classes, metric measure space, embedding theorems, Gagliardo–Nirenberg inequalities.

UDC: 517.518+517.518.23

MSC: 35R30

Received: 06.07.2017

DOI: 10.17377/smzh.2018.59.114

 English version: Siberian Mathematical Journal, 2018, 59:1, 126–135

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