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Weak type inequality for the maximal operator of the (C, α) means of two-dimensionalWalsh-Fourier series

Неравеиство слабого типа для максимального оператора (C, α)-цредних двумерныы рядов Фурье-Уолша

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Abstract

The main aim of this paper is to prove that the maximal operator σ α* of the (C, α) means of the cubical partial sums of the two-dimensional Walsh-Fourier series is bounded from the Hardy space H 2/(2+α) to the space weak-L 2/(2+α).

Резюме

Основной результат работы состоит в доказательстве, что максимальный оператор σ α* для (C, α)-средних частных сумм по квадратам двумерных рядов Фурье-Уолша ограничен из пространства Харди H 2/(2+α) в слабое пространство L 2/(2+α).

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Street 1, Tbilisi, 0128, Georgia

    Ushangi Goginava

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  1. Ushangi Goginava
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Correspondence to Ushangi Goginava.

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The author was supported by the Georgian National Foundation for Scientific Research, Grant GNSF/ST08/3-385.

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Goginava, U. Weak type inequality for the maximal operator of the (C, α) means of two-dimensionalWalsh-Fourier series. Anal Math 36, 1–31 (2010). https://doi.org/10.1007/s10476-010-0101-9

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  • DOI: https://doi.org/10.1007/s10476-010-0101-9

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