Open AccessSobolev embeddings in metric measure spaces with variable dimension
Author(s) -
Petteri Harjulehto,
Peter Hästö,
Visa Latvala
Publication year - 2006
Publication title -
mathematische zeitschrift
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.38
H-Index - 66
eISSN - 1432-1823
pISSN - 0025-5874
DOI - 10.1007/s00209-006-0960-8
Subject(s) - mathematics , sobolev space , measure (data warehouse) , lp space , sobolev inequality , dimension (graph theory) , pure mathematics , metric space , birnbaum–orlicz space , metric (unit) , interpolation space , variable (mathematics) , type (biology) , discrete mathematics , mathematical analysis , functional analysis , banach space , ecology , biochemistry , chemistry , operations management , database , biology , computer science , economics , gene
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.
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