Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings

Alexander Menovschikov; Alexander Ukhlov

doi:10.1007/s10958-021-05549-2

Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings

Alexander Menovschikov, Alexander Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces, we prove that BMO-quasiconformal mappings generate bounded composition operators from Hardy–Sobolev spaces to Sobolev spaces.

Original language	English
Pages (from-to)	313-325
Number of pages	13
Journal	Journal of Mathematical Sciences
Volume	258
Issue number	3
DOIs	https://doi.org/10.1007/s10958-021-05549-2
State	Published - 1 Oct 2021

Keywords

Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-021-05549-2

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abstract = "In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces, we prove that BMO-quasiconformal mappings generate bounded composition operators from Hardy–Sobolev spaces to Sobolev spaces.",

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N2 - In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces, we prove that BMO-quasiconformal mappings generate bounded composition operators from Hardy–Sobolev spaces to Sobolev spaces.

AB - In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces, we prove that BMO-quasiconformal mappings generate bounded composition operators from Hardy–Sobolev spaces to Sobolev spaces.

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KW - Sobolev spaces

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Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings

Abstract

Keywords

ASJC Scopus subject areas

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