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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On interpolation in NEXT(KB.Alt(2))

100%
Kostrzycka Z.
Bulletin of the Section of Logic
|
2018
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tom 47
|
nr 3
EN
We prove that there is infinitely many tabular modal logics extending KB.Alt(2) which have interpolation.
2
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Packing in Orlicz sequence spaces

100%
Rao M. M., Ren Z. D.
Studia Mathematica
|
1997
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tom 126
|
nr 3
235-251
EN
We show how one can, in a unified way, calculate the Kottman and the packing constants of the Orlicz sequence space defined by an N-function, equipped with either the gauge or Orlicz norms. The values of these constants for a class of reflexive Orlicz sequence spaces are found, using a quantitative index of N-functions and some interpolation theorems. The exposition is essentially selfcontained.
3
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Partial retractions for weighted Hardy spaces

100%
Kisliakov S., Xu Q.
Studia Mathematica
|
2000
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tom 138
|
nr 3
251-264
EN
Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^{-1})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.
4
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On some generalization of box splines

100%
Wronicz Z.
Annales Polonici Mathematici
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1999
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tom 72
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nr 3
261-271
EN
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
5
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$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative

88%
Weisz F.
Studia Mathematica
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1996
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tom 120
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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.
6
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Fejér means of two-dimensional Fourier transforms on $H_p(ℝ × ℝ)$

88%
Weisz F.
Colloquium Mathematicum
|
1999
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tom 82
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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.
7
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Domination, independence and irredundance in graphs

78%
Topp J.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction........................................................................................................ 5  1.1. Purpose and scope................................................................................. 5  1.2. Basic graphtheoretical terms................................................................ 6 2. Domination, independence and irredundance in graphs................................ 9  2.1. Introduction and preliminaries.............................................................. 9  2.2. Domination parameters of vertex and edgedeleted subgraphs..... 15  2.3. Packing and covering numbers............................................................ 25  2.4. Conditions for equalities of domination parameters........................ 35 3. Well covered graphs........................................................................................ 46  3.1. Introduction and preliminary results..................................................... 46  3.2. The well coveredness of products of graphs..................................... 55  3.3. Well covered simplicial and chordal graphs...................................... 67  3.4. Well covered line and total graphs....................................................... 73  3.5. Well covered generalized Petersen graphs........................................ 78  3.6. Well irredundant graphs......................................................................... 80 4. Graphical sequences and sets of integers......................................................... 85  4.1. Dominationfeasible sequences........................................................... 86  4.2. Interpolation properties of domination parameters.......................... 91 References.................................................................................................................... 94
8
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Riesz means of Fourier transforms and Fourier series on Hardy spaces

75%
Weisz F.
Studia Mathematica
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1998
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tom 131
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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.
9
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A Carlson type inequality with blocks and interpolation

75%
Ya Kruglyak N., Maligranda L., Persson L. E.
Studia Mathematica
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1993
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tom 104
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nr 2
161-180
EN
An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of "blocks" and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre's interpolation functor $⟨⟩_{φ}$ (see [26]) and its Gagliardo closure on couples of functional Banach lattices in terms of the Calderón-Lozanovskiǐ construction. Our interest in this functor is inspired by the fact that if $φ = t^{θ}(0 < θ < 1)$, then, on couples of Banach lattices and their retracts, it coincides with the complex method (see [20], [27]) and, thus, it may be regarded as a "real version" of the complex method.
10
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Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate

75%
Maffezioli P., Orlandelli E.
Bulletin of the Section of Logic
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2019
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tom 48
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nr 2
137-158
EN
In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and (partly) overcome the failure of interpolation for the implication-free fragment.
11
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Cesàro summability of one- and two-dimensional trigonometric-Fourier series

75%
Weisz F.
Colloquium Mathematicum
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1997
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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.
12
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Distribution and rearrangement estimates of the maximal function and interpolation

63%
U. Asekritova I., Krugljak N. Y., Maligranda L., Persson L.-E.
Studia Mathematica
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1997
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tom 124
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nr 2
107-132
EN
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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