Foundations of Quasiconformal Mappings

Cazacu, Cabiria Andreian

doi:10.1016/s1874-5709(05)80021-6

Cited by 9 publications

(1 citation statement)

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“…The important notion of p-modulus is inherent in defining and studying Newtonian spaces. Recall that p-modulus of a family of curves in the Euclidean space R n is a generalization of the n-modulus, a conformal invariant which is an essential tool in the geometric function theory, in particular in the theory of quasiconformal and quasiregular mappings [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A generalization of Orlicz–Sobolev spaces on metric measure spaces via Banach function spaces

Mocanu

2010

Complex Variables and Elliptic Equations

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To cite this article: Marcelina Mocanu (2010) A generalization of Orlicz-Sobolev spaces on metric measure spaces via Banach function spaces, Complex Variables andWe show that several basic definitions and results regarding modulus, capacity and Orlicz-Sobolev spaces on metric measure spaces can be generalized to the case where the role of the Orlicz space is played by an abstract Banach function space B. This new general setting could bring a new perspective in the study of Sobolev-type spaces on metric measure spaces, due to the great generality of Banach function spaces. We prove several properties of the newly introduced Sobolev-type space N 1,B (X ), including its completeness and a Mazur-type theorem.

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Section: Introductionmentioning

confidence: 99%