Author:
Baramidze David,Persson Lars-Erik,Tangrand Kristoffer,Tephnadze George
Abstract
AbstractWe investigate the subsequence $\{t_{2^{n}}f \}$
{
t
2
n
f
}
of Nörlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces $H_{p}$
H
p
to the space $\mathit{weak-}L_{p} $
w
e
a
k
−
L
p
for $0< p<1/(1+\alpha ) $
0
<
p
<
1
/
(
1
+
α
)
, where $0<\alpha <1$
0
<
α
<
1
. Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Nörlund logarithmic means and Cesàro means.
Funder
Shota Rustaveli National Science Foundation
UiT The Arctic University of Norway
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference31 articles.
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