On some \((H_{p,q},L_{p,q})\)-type maximal inequalities with respect to the Walsh-Paley system (Q2702980)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On some \((H_{p,q},L_{p,q})\)-type maximal inequalities with respect to the Walsh-Paley system |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some \((H_{p,q},L_{p,q})\)-type maximal inequalities with respect to the Walsh-Paley system |
scientific article |
Statements
2 July 2001
0 references
\(p\)-atom
0 references
atomic decomposition
0 references
\(p\)-quasi-local operator
0 references
maximal operator
0 references
multiple Walsh-Fourier series
0 references
martingale Hardy-Lorentz space
0 references
Cesàro means
0 references
On some \((H_{p,q},L_{p,q})\)-type maximal inequalities with respect to the Walsh-Paley system (English)
0 references
It is proved that the maximal operator of the Cesàro means of a multiple Walsh-Fourier series is bounded from the martingale Hardy-Lorentz space \(H_{p,q}\) to \(L_{p,q}\) and is of weak type \((L_1, L_1)\), provided that the supremum in the maximal operator is taken over a positive cone. Moreover, it is obtained that the Cesàro means of a function \(f\in L_1\) converge a.e. to the function in question.NEWLINENEWLINENEWLINENote that the same results are also proved in [\textit{F. Weisz}, ``Maximal estimates for the \((C,\alpha)\) means of \(d\)-dimensional Walsh-Fourier series'', Proc. Am. Math. Soc. 128, No. 8, 2337-2345 (2000; Zbl 0973.42019)].
0 references
