Temat: atom - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: $(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative
Autorzy:: Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/1287322.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Hardy spaces
p-atom
interpolation
Walsh functions
dyadic derivative
Opis:: It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space $H_{p,q}$ to $L_{p,q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $(L_1,L_1)$. As a consequence we show that the dyadic integral of a ∞ function $f ∈ L_1$ is dyadically differentiable and its derivative is f a.e.
Źródło:: Studia Mathematica; 1996, 120, 3; 271-288
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Fejér means of two-dimensional Fourier transforms on $H_p(ℝ × ℝ)$
Autorzy:: Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/1396031.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: p-atom
Hardy spaces
atomic decomposition
interpolation
Fejér means
Opis:: The two-dimensional classical Hardy spaces $H_p(ℝ × ℝ)$ are introduced and it is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from $H_p(ℝ × ℝ)$ to $L_p(ℝ^2)$ (1/2 < p ≤ ∞) and is of weak type $(H^{#}_1 (ℝ × ℝ), L_1(ℝ^2))$ where the Hardy space $H^#_1(ℝ × ℝ)$ is defined by the hybrid maximal function. As a consequence we deduce that the Fejér means of a function f ∈ $H_1^#(ℝ × ℝ)$ ⊃ $LlogL(ℝ^2)$ converge to f a.e. Moreover, we prove that the Fejér means are uniformly bounded on $H_p(ℝ × ℝ)$ whenever 1/2 < p < ∞. Thus, in case f ∈ $H_p(ℝ × ℝ)$, the Fejér means converge to f in $H_p(ℝ × ℝ)$ norm (1/2 < p < ∞). The same results are proved for the conjugate Fejér means.
Źródło:: Colloquium Mathematicum; 1999, 82, 2; 155-166
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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

Skocz do pozycji: 4.

Tytuł:: Riesz means of Fourier transforms and Fourier series on Hardy spaces
Autorzy:: Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/1217804.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Hardy spaces
p-atom
atomic decomposition
interpolation
Fourier transforms
Riesz means
Opis:: Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_p(ℝ)$ to $L_p(ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_p(ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ ∈ L_1(ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_p(ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ ∈ H_p(ℝ)$, the Riesz means converge to ⨍ in $H_p(ℝ)$ norm (1/(α+1) < p < ∞). The same results are proved for the conjugate Riesz means and for Fourier series of distributions.
Źródło:: Studia Mathematica; 1998, 131, 3; 253-270
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Cesàro summability of one- and two-dimensional trigonometric-Fourier series
Autorzy:: Weisz, Ferenc
Powiązania:: https://bibliotekanauki.pl/articles/966758.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: p-atom
Hardy spaces
Cesàro summability
atomic decomposition
p-quasilocal operator
interpolation
Opis:: We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from $L_∞$ to $L_∞$ then it is also bounded from the classical Hardy space $H_p(T)$ to $L_p$ (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from $H_p(T)$ to $L_p$ (3/4 < p ≤ ∞) and is of weak type $(L_1,L_1)$. We define the two-dimensional dyadic hybrid Hardy space $H_{1}^{♯}(T^2)$ and verify that the maximal operator of the Cesàro means of a two-dimensional function is of weak type $(H_{1}^{♯}(T^2),L_1)$. So we deduce that the two-parameter Cesàro means of a function $f ∈ H_1^{♯}(T^2) ⊃ Llog L$ converge a.e. to the function in question.
Źródło:: Colloquium Mathematicum; 1997, 74, 1; 123-133
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

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

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