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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 389, Pages 257–282 (Mi znsl4129)  
Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk

F. A. Shamoyan

I. G. Petrovsky Bryansk State University, Bryansk, Russia
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Abstract: A complete description is found for functions $h$ integrable on the unit circle and having the property that the Toeplitz operator whose symbol is $h$ is bounded in certain weighted Sobolev spaces of functions holomorphic in the disk.
Key words and phrases: unit disk, holomorphic function, Sobolev space, Toeplitz operator, Zygmund space.
Received: 05.05.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 182, Issue 5, Pages 727–742
DOI: https://doi.org/10.1007/s10958-012-0777-4
Bibliographic databases:
Document Type: Article
UDC: 517.547+517.98
Language: Russian
Citation: F. A. Shamoyan, “Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk”, Investigations on linear operators and function theory. Part 39, Zap. Nauchn. Sem. POMI, 389, POMI, St. Petersburg, 2011, 257–282; J. Math. Sci. (N. Y.), 182:5 (2012), 727–742
Citation in format AMSBIB
\Bibitem{Sha11}
\by F.~A.~Shamoyan
\paper Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk
\inbook Investigations on linear operators and function theory. Part~39
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 389
\pages 257--282
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4129}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 182
\issue 5
\pages 727--742
\crossref{https://doi.org/10.1007/s10958-012-0777-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860357666}
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