V. A. Rodin, “The Hardy-Littlewood theorem for the cosine series in a symmetric space”, Mat. Zametki, 20:2 (1976), 241–246; Math. Notes, 20:2 (1976), 693

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Matematicheskie Zametki, 1976, Volume 20, Issue 2, Pages 241–246 (Mi mzm9986)

This article is cited in 8 scientific papers (total in 8 papers)

The Hardy-Littlewood theorem for the cosine series in a symmetric space

V. A. Rodin

Voronezh State Pedagogical Institute

Full-text PDF (514 kB) Citations (8)

Abstract: For a wide class of functional spaces we obtain a necessary and sufficient condition on a space that guarantees a Hardy–Littlewood type of assertion about whether the sum of a cosine series with monotonic coefficients belongs to a functional space, e.g.,

L_{p}

$L_p$ (

p > 1

$p>1$ ). As examples we consider Lorentz spaces, Marcinkiewicz spaces, Orlicz spaces, and

L_{p}

$L_p$ spaces.

Received: 18.10.1974

English version:
Mathematical Notes, 1976, Volume 20, Issue 2, Pages 693–696
DOI: https://doi.org/10.1007/BF01155876

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: V. A. Rodin, “The Hardy-Littlewood theorem for the cosine series in a symmetric space”, Mat. Zametki, 20:2 (1976), 241–246; Math. Notes, 20:2 (1976), 693–696

Citation in format AMSBIB

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\by V.~A.~Rodin

\paper The Hardy-Littlewood theorem for the cosine series in a symmetric space

\jour Mat. Zametki

\yr 1976

\vol 20

\issue 2

\pages 241--246

\mathnet{http://mi.mathnet.ru/mzm9986}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=427931}

\zmath{https://zbmath.org/?q=an:0338.42010}

\transl

\jour Math. Notes

\yr 1976

\vol 20

\issue 2

\pages 693--696

\crossref{https://doi.org/10.1007/BF01155876}

Linking options:

https://www.mathnet.ru/eng/mzm9986

https://www.mathnet.ru/eng/mzm/v20/i2/p241

This publication is cited in the following 8 articles:

G. A. Akishev, “O tochnosti neravenstva raznykh metrik dlya trigonometricheskikh polinomov v obobschennom prostranstve Lorentsa”, Tr. IMM UrO RAN, 25, no. 2, 2019, 9–20
G. A. Akishev, “Neravenstvo raznykh metrik v obobschennom prostranstve Lorentsa”, Tr. IMM UrO RAN, 24, no. 4, 2018, 5–18
A. U. Bimendina, E. S. Smailov, “Fourier–Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$ , $1<p<+\infty$ , $1<\theta<+\infty$ ”, Proc. Steklov Inst. Math., 293 (2016), 77–98
M. I. Dyachenko, E. D. Nursultanov, “Hardy-Littlewood theorem for trigonometric series with $\alpha$ -monotone coefficients”, Sb. Math., 200:11 (2009), 1617–1631
Volosivets S.S., “On Hardy and Bellman Transforms of Series with Respect to Multiplicative Systems in Symmetric Spaces”, Anal. Math., 35:2 (2009), 131–148
E. D. Nursultanov, “Nikol'skii's Inequality for Different Metrics and Properties of the Sequence of Norms of the Fourier Sums of a Function in the Lorentz Space”, Proc. Steklov Inst. Math., 255 (2006), 185–202
E. D. Nursultanov, “On the coefficients of multiple Fourier series in $L_p$ -spaces”, Izv. Math., 64:1 (2000), 93–120
O. Ya. Berchiyan, “On Hardy and Bellman transforms of the Fourier coefficients of functions in symmetric spaces”, Math. Notes, 53:4 (1993), 361–366

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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