- Tytuł:
- Two-parameter Hardy-Littlewood inequalities
- Autorzy:
- Weisz, Ferenc
- Powiązania:
- https://bibliotekanauki.pl/articles/1287705.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Hardy spaces
rectangle p-atom
atomic decomposition
Hardy-Littlewood inequalities - Opis:
- The inequality (*) $(∑_{|n|=1}^{∞} ∑_{|m|=1}^{∞} |nm|^{p-2} |f̂(n,m)|^p)^{1/p} ≤ C_p ∥ƒ∥_{H_p}$ (0 < p ≤ 2) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space $H_p$ on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in $L_p$ whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from $H_1$ converges a.e. and also in $L_1$ norm to that function.
- Źródło:
-
Studia Mathematica; 1996, 118, 2; 175-184
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł