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  • 1 Inst. of Math. and Comp. Sci., College of Nyíregyháza, Nyíregyháza, P.O.Box 166., H–4400, Hungary
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Abstract

The aim of this paper is to prove the a.e. convergence of sequences of the Fejér means of the Walsh–Fourier series of bivariate integrable functions. That is, let such that aj(n+1)≧δsupknaj(n) (j=1,2, n∊ℕ) for some δ>0 and a1(+∞)=a2(+∞)=+∞. Then for each integrable function fL1(I2) we have the a.e. relation . It will be a straightforward and easy consequence of this result the cone restricted a.e. convergence of the two-dimensional Walsh–Fejér means of integrable functions which was proved earlier by the author and Weisz [3,8].

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  • [4] Gát, G. 2000 On the divergence of the (C,1) means of double Walsh–Fourier series Proc. Am. Math. Soc. 128 17111720 .

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  • [8] Weisz, F. 1996 Cesàro summability of two-dimensional Walsh–Fourier series Trans. Amer. Math. Soc. 348 21692181 .

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  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
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CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)