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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 222, Pages 151–162 (Mi znsl4313)  
This article is cited in 3 scientific papers (total in 3 papers)

Weighted estimates of the Fourier transformation

O. G. Parfenov

Pskov State Pedagogical Institute
Full-text PDF (455 kB) Citations (3)
Abstract: The Fourier transformation is regarded as an operator from $\mathcal L_2(-\pi,\pi)$ to $\mathcal L_2(\mathbb R,\mu)$, where $\mu$ is a measure on the real axis $\mathbb R$. Some criteria are obtained for this operator to be bounded or compact, or to belong to some symmetrically normed ideal with the domination property. These results can be viewed as a description of the Carleson measures for the Paley–Wiener space of entire functions. Bibliography: 15 titles.
Received: 01.10.1994
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 5, Pages 3878–3885
DOI: https://doi.org/10.1007/BF02355829
Bibliographic databases:
Document Type: Article
UDC: 517.43
Language: Russian
Citation: O. G. Parfenov, “Weighted estimates of the Fourier transformation”, Investigations on linear operators and function theory. Part 23, Zap. Nauchn. Sem. POMI, 222, POMI, St. Petersburg, 1995, 151–162; J. Math. Sci. (New York), 87:5 (1997), 3878–3885
Citation in format AMSBIB
\Bibitem{Par95}
\by O.~G.~Parfenov
\paper Weighted estimates of the Fourier transformation
\inbook Investigations on linear operators and function theory. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 222
\pages 151--162
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4313}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1359997}
\zmath{https://zbmath.org/?q=an:0909.42003|0889.42006}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 5
\pages 3878--3885
\crossref{https://doi.org/10.1007/BF02355829}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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