Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 17

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Multi-dimensional Fejér summability and local Hardy spaces

100%
Weisz F.
Studia Mathematica
|
2009
|
tom 194
|
nr 2
181-195
EN
It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space $W(h_{p},ℓ_{∞})$ to $W(L_{p},ℓ_{∞})$. This implies the almost everywhere convergence of the Fejér means in a cone for all $f ∈ W(L₁,ℓ_{∞})$, which is larger than $L₁(ℝ^{d})$.
2
Content available remote

Riesz means of Fourier transforms and Fourier series on Hardy spaces

100%
Weisz F.
Studia Mathematica
|
1998
|
tom 131
|
nr 3
253-270
EN
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.
3
Content available remote

Two-parameter Hardy-Littlewood inequalities

100%
Weisz F.
Studia Mathematica
|
1996
|
tom 118
|
nr 2
175-184
EN
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.
4
Content available remote

Some footprints of Marcinkiewicz in summability theory

100%
Weisz F.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
399-413
EN
Four basic results of Marcinkiewicz are presented in summability theory. We show that setting out from these theorems many mathematicians have reached several nice results for trigonometric, Walsh- and Ciesielski-Fourier series.
5
Content available remote

On the Fejér means of bounded Ciesielski systems

100%
Weisz F.
Studia Mathematica
|
2001
|
tom 146
|
nr 3
227-243
EN
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space $H_{p}$ to $L_{p}$ if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.
6
Content available remote

Martingale operators and Hardy spaces generated by them

100%
Weisz F.
Studia Mathematica
|
1995
|
tom 114
|
nr 1
39-70
EN
Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space $H_{p}^{T}$ is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the $BMO_q$ spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the $L_p$ norm of the sharp operator is equivalent to the $H_{p}^{T}$ norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method. Martingale inequalities between Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation and for the conditional q-variation. The duals of the Hardy spaces generated by these special operators are characterized.
7
Content available remote

Conjugate martingale transforms

100%
Weisz F.
Studia Mathematica
|
1992
|
tom 103
|
nr 2
207-220
EN
Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.
8
Content available remote

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

100%
Weisz F.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 2
173-194
EN
The martingale Hardy space $H_p([0,1)^2)$ and the classical Hardy space $H_p(𝕋^2)$ 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.
9
Content available remote

An application of two-parameter martingales in harmonic analysis

100%
Weisz F.
Studia Mathematica
|
1993
|
tom 107
|
nr 2
115-126
EN
Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.
10
Content available remote

Results on spline-Fourier and Ciesielski-Fourier series

100%
Weisz F.
Banach Center Publications
|
2006
|
tom 72
|
nr 1
367-383
EN
Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series and Hardy spaces is studied.
11
Content available remote

$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative

100%
Weisz F.
Studia Mathematica
|
1996
|
tom 120
|
nr 3
271-288
EN
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.
12
Content available remote

Strong summability of Ciesielski-Fourier series

100%
Weisz F.
Studia Mathematica
|
2004
|
tom 161
|
nr 3
269-302
EN
A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).
13
Content available remote

Fejér means of two-dimensional Fourier transforms on $H_p(ℝ × ℝ)$

100%
Weisz F.
Colloquium Mathematicum
|
1999
|
tom 82
|
nr 2
155-166
EN
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.
14
Content available remote

An extension of an inequality due to Stein and Lepingle

100%
Weisz F.
Colloquium Mathematicum
|
1996
|
tom 71
|
nr 1
55-61
EN
Hardy spaces consisting of adapted function sequences and generated by the q-variation and by the conditional q-variation are considered. Their dual spaces are characterized and an inequality due to Stein and Lepingle is extended.
15
Content available remote

Cesàro summability of one- and two-dimensional trigonometric-Fourier series

100%
Weisz F.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 1
123-133
EN
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.
16
Content available remote

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

64%
Simon P., Weisz F.
Studia Mathematica
|
1997
|
tom 125
|
nr 3
231-246
EN
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.
17
Content available remote

Inequalities relative to two-parameter Vilenkin-Fourier coefficients

38%
Weisz F.
Studia Mathematica
|
1991
|
tom 99
|
nr 3
221-233
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.