二维Walsh-Fourier级数的Marcinkiewicz型加权极大算子Cesàro均值

Pub Date : 2023-01-01 DOI:10.2298/fil2309981b

István Blahota, Károly Nagy

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引用次数: 0

摘要

本文研究Marcinkiewicz型(C，?)-means ??的加权极大算子的行为。，* p (f):= supn?P | ? ? n (f) | / n2 / P ?(2 +)哈代空间惠普(G2) (0 & lt;？ & lt;1和p <2/(2 + ?))证明了极大算子??，* p(f)从并矢Hardy空间Hp(G2)有界到Lebesgue空间Lp(G2)，这在某种意义上是尖锐的。并在Hp(G2)中证明了Walsh-Fourier级数的Marcinkiewicz型(C， ?)均值的一个强收敛定理。

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On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series

In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in the Hardy space Hp(G2) (0 < ? < 1 and p < 2/(2 + ?)). It is showed that the maximal operators ??,* p (f) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, ?) means of Walsh-Fourier series in Hp(G2).

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