Geodesic
On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series
Filomat, Tome 37 (2023) no. 9, p. 2981

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In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,α)-means σα,∗p ( f ) := supn∈P |σαn ( f )| n2/p−(2+α) in the Hardy space Hp(G 2) (0 α 1 and p 2/(2 + α)). It is showed that the maximal operators σα,∗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, α) means of Walsh-Fourier series in Hp(G2).
DOI : 10.2298/FIL2309981B
Classification : 42C10
Keywords: Walsh-Paley system, maximal operator, Cesàro mean, Hardy space, bounded operator, strong summation 
István Blahota; Károly Nagy. On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series. Filomat, Tome 37 (2023) no. 9, p. 2981 . doi: 10.2298/FIL2309981B
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     author = {Istv\'an Blahota and K\'aroly Nagy},
     title = {On the weighted maximal operators of {Marcinkiewicz} type {Ces\`aro} means of two-dimensional {Walsh-Fourier} series},
     journal = {Filomat},
     pages = {2981 },
     year = {2023},
     volume = {37},
     number = {9},
     doi = {10.2298/FIL2309981B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309981B/}
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