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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 3–14 (Mi izv333)  

This article is cited in 11 scientific papers (total in 11 papers)

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

B. I. Golubov

Moscow Engineering Physics Institute (State University)

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.

DOI: https://doi.org/10.4213/im333

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English version:
Izvestiya: Mathematics, 2001, 65:3, 425–435

Bibliographic databases:

MSC: 2605, 3505, 42C05, 42C10, 43A75, 42C10
Received: 17.05.2000

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
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\crossref{https://doi.org/10.4213/im333}
\mathscinet{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746856406}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. I. Golubov, “A modified strong dyadic integral and derivative”, Sb. Math., 193:4 (2002), 507–529  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. B. I. Golubov, “A dyadic analogue of Wiener's Tauberian theorem and some related questions”, Izv. Math., 67:1 (2003), 29–53  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. B. I. Golubov, “Fractional Modified Dyadic Integral and Derivative on $\mathbb{R}_+$”, Funct. Anal. Appl., 39:2 (2005), 64–70  mathnet  crossref  crossref  mathscinet  zmath
    4. S. S. Volosivets, “A modified $\mathbf P$-adic integral and a modified $\mathbf P$-adic derivative for functions defined on a half-axis”, Russian Math. (Iz. VUZ), 49:6 (2005), 25–36  mathnet  mathscinet  zmath  elib
    5. B. I. Golubov, “Modified Dyadic Integral and Fractional Derivative on $\mathbb R_+$”, Math. Notes, 79:2 (2006), 196–214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. B. I. Golubov, “Dyadic distributions”, Sb. Math., 198:2 (2007), 207–230  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Golubov, BI, “On approximation by convolutions and bases of shifts of a function”, Analysis Mathematica, 34:1 (2008), 9  crossref  mathscinet  zmath  isi  elib  scopus
    8. Golubov, BI, “ON THE INTEGRABILITY AND UNIFORM CONVERGENCE OF MULTIPLICATIVE Fourier TRANSFORMS”, Georgian Mathematical Journal, 16:3 (2009), 533  mathscinet  zmath  isi  elib
    9. S. S. Volosivets, “Modified Hardy and Hardy–Littlewood operators and their behaviour in various spaces”, Izv. Math., 75:1 (2011), 29–51  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Igenberlina A., Matin D., Turgumbayev M., “On the Estimate of Deviations of Partial Sums of a Multiple Fourier-Walsh Series of the Form S (2J,) (...) (,2J) F(X) of a Function in the Metric l-1(Q(K))”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 030008  crossref  isi  scopus
    11. S. S. Platonov, “An Analog of Titchmarsh's Theorem for the Fourier–Walsh Transform”, Math. Notes, 103:1 (2018), 96–103  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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