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Fractional Hajłasz-Morrey-Sobolev spaces on quasi-metric measure spaces

Wen Yuan, Yufeng Lu, Dachun Yang (2015)

Studia Mathematica

In this article, via fractional Hajłasz gradients, the authors introduce a class of fractional Hajłasz-Morrey-Sobolev spaces, and investigate the relations among these spaces, (grand) Morrey-Triebel-Lizorkin spaces and Triebel-Lizorkin-type spaces on both Euclidean spaces and RD-spaces.

Fractional iteration in the disk algebra: prime ends and composition operators.

Manuel D. Contreras, Santiago Díaz-Madrigal (2005)

Revista Matemática Iberoamericana

In this paper we characterize the semigroups of analytic functions in the unit disk which lead to semigroups of operators in the disk algebra. These characterizations involve analytic as well as geometric aspects of the iterates and they are strongly related to the classical theorem of Carathéodory about local connection and boundary behaviour of univalent functions.

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