Pointwise convergence of Marcinkiewicz-Fejér means of double Vilenkin-Fourier series
نویسندگان
چکیده
منابع مشابه
Pointwise convergence of Fourier series
In the early 19 century, J. Fourier was an impassioned advocate of the use of such sums, of course writing sines and cosines rather than complex exponentials. Euler, the Bernouillis, and others had used such sums in similar fashions and for similar ends, but Fourier made a claim extravagant for the time, namely that all functions could be expressed in such terms. Unfortunately, in those days th...
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Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1,1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...
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In the present paper we prove that for any 0 < p ≤ 2/3 there exists a martingale f in Hp such that the Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series of the martingale f is not uniformly bounded in the space Lp .
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متن کاملConvergence and Divergence of Fejér Means of Fourier Series on One and Two-Dimensional Walsh and Vilenkin Groups
It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fejér (or (C,1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a résumé of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too.
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ژورنال
عنوان ژورنال: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
سال: 2017
ISSN: 1068-3623,1934-9416
DOI: 10.3103/s1068362317050041