On the maximal operators of Fejér means with respect to the character system of the group of 2-adic integers in hardy spaces

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• 作者：G. Gát ; K. Nagy
• 关键词：group of 2 ; adic integers ; character system ; Fejér mean ; Fourier series ; Hardy space ; maximal operator
• 刊名：Mathematical Notes
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：98
• 期：1-2
• 页码：68-77
• 全文大小：675 KB
• 参考文献：1.M. H. Taibleson, Fourier Analysis on Local Fields (Princeton Univ. Press., Princeton, 1975).MATH
  2.F. Schipp and W. R. Wade, Norm convergence and summability of Fourier Series with Respect to Certain Product Systems, in Pure and Appl. Math. Approx. Theory (Marcel Dekker, New York–Basel–Hong Kong, 1992), Vol. 138.
  3.G. Gát, “On the almost everywhere convergence of Fejérmeans of functions on the group of 2-adic integers,-J. Approx. Theory 90, 88-6 (1997).MATH MathSciNet CrossRef
  4.G. Gát, “Almost everywhere convergence of Cesàro means of Fourier series on the group of 2-adic integers,-Acta Math. Hungar. 116 (3), 209-21 (2007).MATH MathSciNet CrossRef
  5.G. Gát, “On the Fejér kernel functions with respect to the character system of the group of 2-adic integers,-Annales Univ. Sci. Budapest., Sec. Comp. 40, 257-67 (2013).MATH
  6.I. Blahota and G. Gát, “Pointwise convergence of double Vilenkin-Fejérmeans,-Studia Sci.Math. Hungar. 36, 49-3 (2000).MATH MathSciNet
  7.K. Nagy, “Almost everywhere convergence of cone-like restricted two-dimensional Fejér means with respect to Vilenkin-like systems,-Algebra i Analiz 25 (4), 125-38 (2013) [St. PetersburgMath. J. 25 (4), 605-14 (2014)].
  8.I. Blahota, “Almost everywhere convergence of subsequence of logarithmic means of Fourier series on the group of 2-adic integers,-Georgian Math. J. 19 (3), 417-25 (2012).MATH MathSciNet CrossRef
  9.F. Schipp, W. R. Wade, P. Simon, and J. Pá l, Walsh Series: An Introduction to Dyadic Harmonic Analysis (Adam Hilger, Bristol–New York, 1990).MATH
  10.F. Schipp and W. R. Wade, Transforms on Normed Fields (Janus Pannonius Tudomá nyegyetem, Pécs, 1995).
  11.E. Hewitt and K. Ross, Abstract Harmonic Analysis (Springer–Verlag, Heidelberg, 1963), Vols. I, II.MATH CrossRef
  12.F. Weisz, Summability of Multi-Dimensional Fourier Series and Hardy Space (Kluwer Academic, Dordrecht, 2002).CrossRef
  13.P. Simon, “Cesàro summability with respect to two-parameter Walsh system,-Monatsh. Math. 131, 321-34 (2000).MathSciNet CrossRef
  
• 作者单位：G. Gát (1)
  K. Nagy (1)
  
  1. College of Nyíregyháza, Nyíregyháza, Hungary
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejér (or (C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Gá t in 1997. The aim of this paper is to investigate the maximal operator of the sup _n |σ _n |. Among other things, we prove that this operator is bounded from the Hardy space H _p to the Lebesgue space L _p if and only if 1/2 < p < ? The two-dimensional maximal operator is also discussed. Keywords group of 2-adic integers character system Fejér mean Fourier series Hardy space maximal operator