V. Gol'dshtein, A. Ukhlov, “Brennan's conjecture for composition operators on Sobolev spaces”, Eurasian Math. J., 3:4 (2012), 35

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Eurasian Mathematical Journal, 2012, Volume 3, Number 4, Pages 35–43 (Mi emj103)

This article is cited in 11 scientific papers (total in 11 papers)

Brennan's conjecture for composition operators on Sobolev spaces

V. Gol'dshtein, A. Ukhlov

Department of Mathematics, Ben-Gurion University of the Negev, Israel

Full-text PDF (404 kB) Citations (11)

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Abstract: We show that Brennan's conjecture is equivalent to the boundedness of composition operators on homogeneous Sobolev spaces, that are generated by conformal homeomorphisms of simply connected plane domains to the unit disc. A geometrical interpretation of Brennan's conjecture in terms of integrability of

$p$ -distortion is given.

Keywords and phrases: Brennan's conjecture, conformal mappings, composition operators, Sobolev spaces.

Received: 20.11.2012

Bibliographic databases:

Document Type: Article

MSC: 30C35, 46E35

Language: English

Citation: V. Gol'dshtein, A. Ukhlov, “Brennan's conjecture for composition operators on Sobolev spaces”, Eurasian Math. J., 3:4 (2012), 35–43

Citation in format AMSBIB

\Bibitem{GolUkh12}

\by V.~Gol'dshtein, A.~Ukhlov

\paper Brennan's conjecture for composition operators on Sobolev spaces

\jour Eurasian Math. J.

\yr 2012

\vol 3

\issue 4

\pages 35--43

\mathnet{http://mi.mathnet.ru/emj103}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3040685}

\zmath{https://zbmath.org/?q=an:1281.30008}

Linking options:

https://www.mathnet.ru/eng/emj103

https://www.mathnet.ru/eng/emj/v3/i4/p35

This publication is cited in the following 11 articles:

Gol'dshtein V., Pchelintsev V., Ukhlov A., “Spectral Properties of the Neumann-Laplace Operator in Quasiconformal Regular Domains”, Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial, Contemporary Mathematics, 734, eds. Kuchment P., Semenov E., Amer Mathematical Soc, 2019, 129–144
Gol'dshtein V., Pchelintsev V., Ukhlov A., “On the First Eigenvalue of the Degenerate -Laplace Operator in Non-Convex Domains”, Integr. Equ. Oper. Theory, 90:4 (2018), UNSP 43
Gol'dshtein V., Pchelintsev V., Ukhlov A., “Spectral Estimates of the P-Laplace Neumann Operator and Brennan'S Conjecture”, Boll. Unione Mat. Ital., 11:2 (2018), 245–264
V. Gol'dshtein, A. Ukhlov, “The spectral estimates for the Neumann–Laplace operator in space domains”, Adv. Math., 315 (2017), 166–193
V. Gol'dshtein, A. Ukhlov, “Weak regularity of degenerate elliptic equations”, Lobachevskii J. Math., 38:2, SI (2017), 262–270
V. I. Burenkov, V. Gol'dshtein, A. Ukhlov, “Conformal spectral stability estimates for the Neumann Laplacian”, Math. Nachr., 289:17-18 (2016), 2133–2146
V. Gol'dshtein, A. Ukhlov, “On the first eigenvalues of free vibrating membranes in conformal regular domains”, Arch. Ration. Mech. Anal., 221:2 (2016), 893–915
V. Gol'dshtein, A. Ukhlov, “Spectral estimates of the $p$-Laplace Neumann operator in conformal regular domains”, Trans. A Razmadze Math. Inst., 170:1 (2016), 137–148
Burenkov V.I., Gol'dshtein V., Ukhlov A., “Conformal Spectral Stability Estimates For the Dirichlet Laplacian”, Math. Nachr., 288:16 (2015), 1822–1833
Gol'dshtein V., Ukhlov A., “Brennan's Conjecture and Universal Sobolev Inequalities”, Bull. Sci. Math., 138:2 (2014), 253–269
Gol'dshtein V., Ukhlov A., “Sobolev Homeomorphisms and Brennan'S Conjecture”, Comput. Methods Funct. Theory, 14:2-3, SI (2014), 247–256

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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