TY - JOUR
T1 - Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series
AU - Gát, György
AU - Goginava, Ushangi
AU - Karagulyan, Grigori
N1 - Publisher Copyright:
© 2014, Akadémiai Kiadó, Budapest, Hungary.
PY - 2014/12
Y1 - 2014/12
N2 - In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.
AB - In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.
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U2 - 10.1007/s10476-014-0401-6
DO - 10.1007/s10476-014-0401-6
M3 - Article
AN - SCOPUS:84919912885
SN - 0133-3852
VL - 40
SP - 243
EP - 266
JO - Analysis Mathematica
JF - Analysis Mathematica
IS - 4
ER -