Walsh-Marcinkiewicz means and Hardy spaces (Q2248118)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Walsh-Marcinkiewicz means and Hardy spaces |
scientific article |
Statements
Walsh-Marcinkiewicz means and Hardy spaces (English)
0 references
30 June 2014
0 references
It is proved that the weighted Marcinkiewicz maximal operator of the two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space \(H_p\) to \(L_p\) if \(0<p<2/3\). It is also shown that the weight function is sharp. As an application two types of convergence of Marcinkiewicz means are investigated, the convergence in Hardy norm and the strong convergence.
0 references
two-dimensional Walsh system
0 references
Marcinkiewicz means
0 references
maximal operator
0 references
dyadic Hardy space
0 references
strong convergence
0 references
modulus of continuity
0 references
0 references
