TY - JOUR
T1 - Two-Dimensional Martingale Transforms and Their Applications in Summability of Walsh–Fourier Series
AU - Goginava, Ushangi
AU - Nagy, Károly
N1 - Publisher Copyright:
© 2023, Mathematica Josephina, Inc.
PY - 2023/8
Y1 - 2023/8
N2 - In the paper, we are going to prove that the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series is bounded from Llog L((0 , 1] × (0 , 1]) to L1,∞((0 , 1] × (0 , 1]) . As a consequence, it can be obtained that Llog L((0 , 1] × (0 , 1]) is maximal Orlicz space, where the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series for the functions from this space converge in measure.
AB - In the paper, we are going to prove that the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series is bounded from Llog L((0 , 1] × (0 , 1]) to L1,∞((0 , 1] × (0 , 1]) . As a consequence, it can be obtained that Llog L((0 , 1] × (0 , 1]) is maximal Orlicz space, where the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series for the functions from this space converge in measure.
KW - Dyadic martingale Hardy space
KW - Marcinkiewicz means
KW - Martingale transform
KW - Nörlund logarithmic mean
KW - Walsh system
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U2 - 10.1007/s12220-023-01307-9
DO - 10.1007/s12220-023-01307-9
M3 - Article
AN - SCOPUS:85159708955
SN - 1050-6926
VL - 33
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 8
M1 - 245
ER -