- Tytuł:
- Two-parameter Hardy-Littlewood inequality and its variants
- Autorzy:
-
Chen, Chang-Pao
Luor, Dah-Chin - Powiązania:
- https://bibliotekanauki.pl/articles/1206123.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Let s* denote the maximal function associated with the rectangular partial sums $s_{mn}(x,y)$ of a given double function series with coefficients $c_{jk}$. The following generalized Hardy-Littlewood inequality is investigated: $||s*||_{p,μ}≤C_{p,α,β} {Σ_{j=0}^∞Σ_{k=0}^∞(j̅ )^{p-α-2}(k̅)^{p-β-2}|c_{jk}|^p }^{1/p}$, where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on $c_{jk}$ and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||_{p,μ}-convergence property of $s_{mn}(x,y)$ is established. These results generalize the work of Askey-Wainger [1], Balashov [2], Boas [3], Chen [5], [6], [8], [9], Marzug [15], Móricz [16]-[18], [19], Móricz-Schipp-Wade [20], Ram-Bhatia [22], Stechkin [24], Weisz [26]-[28], and Young [30].
- Źródło:
-
Studia Mathematica; 2000, 139, 1; 9-27
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł