Non-collapsing condition and Sobolev embeddings for Haj{\l}asz-Besov spaces (original) (raw)
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Revista Matemática Complutense, 2020
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Sobolev embeddings in metric measure spaces with variable dimension
Mathematische Zeitschrift, 2006
In this article we study metric measure spaces with variable dimension. We consider Lebesgue spaces on these sets, and embeddings of the Riesz potential in these spaces. We also investigate Hajłasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.
Embeddings of Besov–Morrey spaces on bounded domains
Studia Mathematica, 2013
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Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2016
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