Wszystkie pola: Hardy inequality - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series
Autorzy:: Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/1288490.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: martingale and classical Hardy spaces
p-atom
atomic decomposition
Walsh functions
Hardy-Littlewood inequality
Opis:: The martingale Hardy space $H_p([0,1)^2)$ and the classical Hardy space $H_p(^2)$ are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from $H_p$ to $L_p$ (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a Marcinkiewicz-Zygmund type inequality is obtained for BMO spaces.
Źródło:: Studia Mathematica; 1995-1996, 117, 2; 173-194
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients
Autorzy:: Simon, Péter
Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/1219101.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: two-parameter martingales and Hardy spaces
rectangle p-atoms
Vilenkin functions
Hardy-Littlewood inequality
Opis:: Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) $(∑_{k=1}^∞ ∑_{j=1}^∞ |f̂(k,j)|^{p}(kj)^{p-2})^{1/p} ≤ C_p∥f∥_{H^p_{**}}$ (1/2 < p≤2) where f belongs to the Hardy space $H_{**}^p (G_m × G_s)$ defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.
Źródło:: Studia Mathematica; 1997, 125, 3; 231-246
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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