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Russian Academy of Sciences. Sbornik. Mathematics, 1995, Volume 82, Issue 2, Pages 327–336
DOI: https://doi.org/10.1070/SM1995v082n02ABEH003567
(Mi sm912)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the Cauchy transform of functionals on a Bergman space

V. V. Napalkov, R. S. Yulmukhametov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
References:
Abstract: The strong dual space of the Bergman space
B2(G)={fH(G):f2B2(G)=G|f(x)|2dv(z)<},
is described in terms of the Cauchy transformation, where v(z) is Lebesgue measure and G is a simply connected domain with boundary of class C1+0. As a normed space, B2(G) is isomorphic to the space
B12(C¯G)={γ(ζ)H(C¯G),γ()=0:γ2B12(C¯G)=C¯G|γ(ζ)|2dv(ζ)<}.
An example is given of a domain with nonsmooth boundary for which the spaces B2(G) and B12(C¯G) are not isomorphic.
Received: 24.06.1993
Bibliographic databases:
UDC: 517.5
MSC: Primary 47G10, 45P05, 46E20; Secondary 30D55, 32H10
Language: English
Original paper language: Russian
Citation: V. V. Napalkov, R. S. Yulmukhametov, “On the Cauchy transform of functionals on a Bergman space”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 327–336
Citation in format AMSBIB
\Bibitem{NapYul94}
\by V.~V.~Napalkov, R.~S.~Yulmukhametov
\paper On the Cauchy transform of functionals on a~Bergman space
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 327--336
\mathnet{http://mi.mathnet.ru/eng/sm912}
\crossref{https://doi.org/10.1070/SM1995v082n02ABEH003567}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1300133}
\zmath{https://zbmath.org/?q=an:0856.46031}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RV83000005}
Linking options:
  • https://www.mathnet.ru/eng/sm912
  • https://doi.org/10.1070/SM1995v082n02ABEH003567
  • https://www.mathnet.ru/eng/sm/v185/i7/p77
  • This publication is cited in the following 4 articles:
    1. Harti El, A. Elkachkouri, A. Ghanmi, “Solid Cauchy transform on the weighted poly-Bergman spaces”, Filomat, 37:3 (2023), 775  crossref
    2. N. F. Abuzyarova, K. P. Isaev, R. S. Yulmukhametov, “Equivalence of norms of analytical functions on exterior of convex domain”, Ufa Math. J., 10:4 (2018), 3–11  mathnet  crossref  isi
    3. K. P. Isaev, R. S. Yulmukhametov, “Laplace transforms of functionals on Bergman spaces”, Izv. Math., 68:1 (2004), 3–41  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. R. S. Yulmukhametov, V. V. Napalkov, “On the Hilbert Transform in Bergman Space”, Math. Notes, 70:1 (2001), 61–70  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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