Author:
Baramidze Davit,Persson Lars-Erik,Tephnadze George
Abstract
AbstractIn this paper we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space $$H_{p}(G)$$
H
p
(
G
)
to the Lebesgue space $$L_{p}(G),$$
L
p
(
G
)
,
for $$0<p<1.$$
0
<
p
<
1
.
Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.
Funder
UiT The Arctic University of Norway
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Theoretical Computer Science,Analysis
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