TY - JOUR
T1 - Convergence in measure of fejér means of two parameter conjugate walsh transforms
AU - Goginava, Ushangi
AU - Said, Salem Ben
N1 - Funding Information:
Acknowledgement. The authors are thankful United Arab Emirates University for financial support through the Start-up Grant No. G00002950.
Publisher Copyright:
© 2021 Element D.O.O.. All rights reserved.
PY - 2021
Y1 - 2021
N2 - Weisz proved-among others – that for f ∈ LlogL the Fejér means σ~n(t,m,u) of conjugate transform of two-parameter Walsh-Fourier series a. e. converges to f(t,u) . The main aim of this paper is to prove that for any Orlicz space, which is not a subspace of LlogL, the set of functions for which Walsh-Fejér Means of two parameter Conjugate Transforms converge in measure is of first Baire category.
AB - Weisz proved-among others – that for f ∈ LlogL the Fejér means σ~n(t,m,u) of conjugate transform of two-parameter Walsh-Fourier series a. e. converges to f(t,u) . The main aim of this paper is to prove that for any Orlicz space, which is not a subspace of LlogL, the set of functions for which Walsh-Fejér Means of two parameter Conjugate Transforms converge in measure is of first Baire category.
KW - Conjugate transform
KW - Convergence in measure
KW - Double Walsh-Fourier series
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U2 - 10.7153/mia-2021-24-09
DO - 10.7153/mia-2021-24-09
M3 - Article
AN - SCOPUS:85103590738
SN - 1331-4343
VL - 24
SP - 115
EP - 128
JO - Mathematical Inequalities and Applications
JF - Mathematical Inequalities and Applications
IS - 1
ER -