Abstract
We introduce Campanato, Morrey, BMO and Sobolev-type spaces for mappings from a space of homogeneous type into a complete metric space which possess properties comparable to their classical analogues. In particular we show integral characterizations, the validity of the John–Nirenberg theorem, Poincare and Sobolev inequalities, Sobolev's embedding theorem and estimates on the pointwise behavior of Sobolev-type mappings.
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