Author:
Baramidze David,Persson Lars-Erik,Singh Harpal,Tephnadze George
Abstract
AbstractWe prove that there exists a martingale $f\in H_{p} $
f
∈
H
p
such that the subsequence $\{L_{2^{n}}f \}$
{
L
2
n
f
}
of Nörlund logarithmic means with respect to the Walsh system are not bounded from the martingale Hardy spaces $H_{p}$
H
p
to the space $weak-L_{p} $
w
e
a
k
−
L
p
for $0< p<1 $
0
<
p
<
1
. We also prove that for any $f\in L_{p}$
f
∈
L
p
, $p\geq 1 $
p
≥
1
, $L_{2^{n}}f$
L
2
n
f
converge to f at any Lebesgue point x. Moreover, some new related inequalities are derived.
Funder
UiT The Arctic University of Norway
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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