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APPROXIMATION BY WALSH-KACZMARZ-FEJR MEANS ON THE HARDY SPACE 被引量:1
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作者 George TEPHNADZE 《Acta Mathematica Scientia》 SCIE CSCD 2014年第5期1593-1602,共10页
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.
关键词 Walsh-Kaczmarz system Fej6r means martingale hardy space modulus ofcontinuity
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The Martingale Hardy Type Inequalities for Dyadic Derivative and Integral 被引量:6
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作者 JianYingNIE Xing Guo Nie GUO Wei LOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第6期1465-1474,共10页
Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of i... Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type (L1,L1), and the corresponding maximal operators of the two-dimensional case are of weak type (Hi, L1). In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1. 展开更多
关键词 martingale hardy space dyadic derivative dyadic integral Walsh-Fejer kernels p-atom quasi-local operator
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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM 被引量:1
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作者 张传洲 刘培德 《Acta Mathematica Scientia》 SCIE CSCD 2009年第1期45-55,共11页
For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequ... For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum. 展开更多
关键词 martingale hardy space Vilenkin-like systems weighted average
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B-Valued Dyadic Derivative 被引量:1
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作者 ZHANG Chuanzhou CHEN Lihong,LIU Peide 《Wuhan University Journal of Natural Sciences》 CAS 2007年第6期961-964,共4页
The principles of the new maximal operator H* we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1) to the Lorentz L^Xp.q[0,1) for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any... The principles of the new maximal operator H* we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1) to the Lorentz L^Xp.q[0,1) for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K (n∈N) is an approximate identity. 展开更多
关键词 martingale hardy space dyadic derivative dyadic integral
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The Martingale Hardy Type Inequality for Marcinkiewicz-Fejer Means of Two-dimensional Conjugate Walsh-Fourier Series
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作者 Ushangi GOGINAVA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第10期1949-1958,共10页
The main aim of this paper is to prove that for any 0 〈 p≤ 2/3 there exists a martingale f E Hp such that Marcinkiewicz Fejer means of the two-dimensional conjugate Walsh Fourier series of the martingale f is not un... The main aim of this paper is to prove that for any 0 〈 p≤ 2/3 there exists a martingale f E Hp such that Marcinkiewicz Fejer means of the two-dimensional conjugate Walsh Fourier series of the martingale f is not uniformly bounded in the space Lp. 展开更多
关键词 Two-dimensional Walsh-Fourier series martingale hardy space Marcinkiewicz Fejer means
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