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Eurasian Math. J., 2012, Volume 3, Number 4, Pages 35–43 (Mi emj103)  

This article is cited in 10 scientific papers (total in 10 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

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.

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Bibliographic databases:
MSC: 30C35, 46E35
Received: 20.11.2012
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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://www.ams.org/mathscinet-getitem?mr=3040685}
\zmath{https://zbmath.org/?q=an:1281.30008}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gol'dshtein V., Ukhlov A., “Brennan's Conjecture and Universal Sobolev Inequalities”, Bull. Sci. Math., 138:2 (2014), 253–269  crossref  mathscinet  zmath  isi  scopus
    2. Gol'dshtein V., Ukhlov A., “Sobolev Homeomorphisms and Brennan'S Conjecture”, Comput. Methods Funct. Theory, 14:2-3, SI (2014), 247–256  crossref  mathscinet  zmath  isi  scopus
    3. Burenkov V.I., Gol'dshtein V., Ukhlov A., “Conformal Spectral Stability Estimates For the Dirichlet Laplacian”, Math. Nachr., 288:16 (2015), 1822–1833  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. I. Burenkov, V. Gol'dshtein, A. Ukhlov, “Conformal spectral stability estimates for the Neumann Laplacian”, Math. Nachr., 289:17-18 (2016), 2133–2146  crossref  mathscinet  zmath  isi  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. V. Gol'dshtein, A. Ukhlov, “The spectral estimates for the Neumann–Laplace operator in space domains”, Adv. Math., 315 (2017), 166–193  crossref  isi
    8. V. Gol'dshtein, A. Ukhlov, “Weak regularity of degenerate elliptic equations”, Lobachevskii J. Math., 38:2, SI (2017), 262–270  crossref  isi
    9. 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  crossref  mathscinet  isi
    10. 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  crossref  mathscinet  zmath  isi  scopus
  • Eurasian Mathematical Journal
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