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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 175–192 (Mi izv341)  

This article is cited in 1 scientific paper (total in 1 paper)

Analogues of the Hausdorff–Young and Hardy–Littlewood theorems

T. V. Rodionov

M. V. Lomonosov Moscow State University

Abstract: We study expansions of functions in the space $L^p$ with respect to systems similar to orthogonal ones. We find estimates for the coefficients and sufficient conditions on them under which the corresponding expansions converge in $L^p$. These results are analogues of the well-known Hausdorff–Young–Riesz and Hardy–Littlewood–Paley theorems in the theory of trigonometric and orthogonal series. It is shown that the resulting estimates are more exact than the classical ones even in the case of orthogonal systems.

DOI: https://doi.org/10.4213/im341

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English version:
Izvestiya: Mathematics, 2001, 65:3, 589–606

Bibliographic databases:

MSC: 42C15, 43A40, 43A32, 47A63
Received: 02.03.2000

Citation: T. V. Rodionov, “Analogues of the Hausdorff–Young and Hardy–Littlewood theorems”, Izv. RAN. Ser. Mat., 65:3 (2001), 175–192; Izv. Math., 65:3 (2001), 589–606

Citation in format AMSBIB
\Bibitem{Rod01}
\by T.~V.~Rodionov
\paper Analogues of the Hausdorff--Young and Hardy--Littlewood theorems
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 175--192
\mathnet{http://mi.mathnet.ru/izv341}
\crossref{https://doi.org/10.4213/im341}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1853371}
\zmath{https://zbmath.org/?q=an:0992.42018}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 589--606
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000341}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746826214}


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    This publication is cited in the following articles:
    1. Degenfeld-Schonburg S., “On the Hausdorff-Young Theorem for Commutative Hypergroups”, Colloq. Math., 131:2 (2013), 219–231  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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