György Gát

Lp-norm convergence of series in compact, totally disconnected groups

AbstractсхОДИМОсть ВLp-НОРМЕ Р ьДОВ НА кОМпАктНых ВпОлНЕ НЕсВьжНых гРУппАх г. гАт И Р. тОлЕДО хОРОшО ИжВЕстНО, ЧтО Ч АстНыЕ сУММы РьДОВ ФУРьЕ-ВИлЕНкИНА Дль к АжДОИ ФУНкцИИf ∃Lp, 1<p<∞, схОДь тсь кf пО НОРМЕ. Дль лУ БОгО 1≤p≤∞ ОпЕРАтОРы

On the pointwise convergence of Cesàro means of two-variable functions with respect to unbounded Vilenkin systems

S_{M_n }

CONVERGENCE IN MEASURE OF LOGARITHMIC MEANS OF DOUBLE WALSH-FOURIER SERIES

тАкжЕ схО Дьтсь пО НОРМЕ кf Дль к АжДОИf ∃Lp.В НАстОьЩЕИ РАБОтЕ Мы ИжУЧАЕМ пОДОБНыЕ сВО ИстВА НА ВпОлНЕ НЕсВьжНых гРУппАх, НЕ ОБьжАтЕль Ных АБЕлЕВых, И Дль сИс тЕМ, сОстОьЩИх Иж пРОИжВЕ ДЕНИИ НОРМИРОВАННых кООРД ИНАтНых ФУНкцИИ Дль Н ЕпРЕРыВНых НЕпРИВОДИМых УНИтАР Ных пРЕДстАВлЕНИИ кООРД ИНАтНых гРУпп. НАкОНЕ ц, Мы УстАНОВлИВАЕМ схОДИ МОсть Дль 1≤p≤∞ сРЕДНИх ФЕИЕ РА В слУЧАЕ ОгРАНИЧЕН Ных гРУпп.

On the logarithmic summability of Fourier series

In 1992, Móricz, Schipp and Wade [MSW] proved for functions in L log+L(I2) (I2 is the unit square) the a.e. convergence of the double (C, 1) means of the Walsh-Fourier series σnf → f as min(n1, n2) → ∞, n = (n1, n2 ∈ N2). In the same paper, they also proved the restricted convergence of the (C, 1) means of functions in L(I2): σ(2n1,2n2)f → f a.e. as min (n1, n2) → ∞ provided |n1 − n2| < C. The aim of this paper is to demonstrate the sharpness of these results of Móricz, Schipp and Wade with respect to both the space L log+L(I2) and the restrictedness |n1 − n2| < C.

On term by term dyadic differentiability of Walsh-Kaczmarz series

One of the most celebrated problems in dyadic harmonic analysis is the pointwise convergence of the Fejer (or (C, 1)) means of functions on unbounded Vilenkin groups. There was no known positive result before the authors paper appeared in 1999 (J. Approx. Theory 101(1) (1999) 1) with respect to the a.e. convergence of the one-dimensional (C, 1) means of Lp (p > 1) functions. This paper is concerned with the almost everywhere convergence of a subsequence of the two-dimensional Fejer means of functions in L log- L. Namely, we prove the a.e. relation limn,k → ∞ σMnċM-k f = f (for the indices the condition |n - k| > α is provided, where α > 0 is some constant).

Calculus on Walsh and Vilenkin Groups

Let

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

G_p

Almost everywhere strong summability of double Walsh-Fourier series

be the