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Izvestiya: Mathematics, 2001, Volume 65, Issue 3, Pages 425–435
DOI: https://doi.org/10.1070/IM2001v065n03ABEH000333 (Mi im333) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On an analogue of Hardy's inequality for the Walsh–Fourier

B. I. Golubov

Moscow Engineering Physics Institute (State University)
English version PDF (159 kB) Citations (12)
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DOI: https://doi.org/10.1070/IM2001v065n03ABEH000333
Abstract: According to Hardy's well-known inequality, the $l_1$-norm of a function in the Hardy space $H(T)$ consisting of $2\pi$-periodic functions serves as an upper estimate for the $l_1$-norm of the sequence of Fourier coefficients of the integral of the function. In this paper, the dyadic Hardy space $H(\mathbb R_+)$ is introduced and an analogue of this estimate is proved for the Walsh–Fourier transform.
Received: 17.05.2000
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2001, Volume 65, Issue 3, Pages 3–14
DOI: https://doi.org/10.4213/im333
Bibliographic databases:
MSC: 2605, 3505, 42C05, 42C10, 43A75, 42C10
Language: English
Original paper language: Russian
Citation: B. I. Golubov, “On an analogue of Hardy's inequality for the Walsh–Fourier”, Izv. RAN. Ser. Mat., 65:3 (2001), 3–14; Izv. Math., 65:3 (2001), 425–435
Citation in format AMSBIB
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\by B.~I.~Golubov
\paper On an analogue of Hardy's inequality for the Walsh--Fourier
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 3--14
\mathnet{http://mi.mathnet.ru/im333}
\crossref{https://doi.org/10.4213/im333}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1853363}
\zmath{https://zbmath.org/?q=an:0992.42015}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 425--435
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000333}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746856406}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:681
    Russian version PDF:271
    English version PDF:52
    References:79
    First page:1
     
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