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    Wyświetlanie 1-10 z 10
    Tytuł:
    Distributional fractional powers of the Laplacean. Riesz potentials
    Autorzy:
    Martínez, Celso
    Sanzi, Miguel
    Periago, Francisco
    Powiązania:
    https://bibliotekanauki.pl/articles/1216946.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    fractional powers
    Laplacean operator
    Riesz potentials
    singular integrals
    Opis:
    For different reasons it is very useful to have at one's disposal a duality formula for the fractional powers of the Laplacean, namely, $((-Δ)^α u,ϕ ) = (u,(-Δ)^α ϕ)$, α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean to obtain some properties of the Riesz potentials in a wide class of spaces which contains the $L^p$-spaces.
    Źródło:
    Studia Mathematica; 1999, 135, 3; 253-271
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Almost everywhere convergence of Laguerre series
    Autorzy:
    Chen, Chang-Pao
    Lin, Chin-Cheng
    Powiązania:
    https://bibliotekanauki.pl/articles/1290468.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    almost everywhere convergence
    Cesàro means
    Laguerre polynomials
    Riesz means
    Opis:
    Let $a ∈ ℤ^+$ and $f ∈ L^p (ℝ^+), 1 ≤ p ≤ ∞ $. Denote by $c_j$ the inner product of f and the Laguerre function $ℒ^a_j$. We prove that if ${c_j}$ satisfies $lim_{λ↓1} \overline lim_{n→∞} ∑_{n
    Źródło:
    Studia Mathematica; 1994, 109, 3; 291-301
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Tytuł:
    Almost everywhere summability of Laguerre series
    Autorzy:
    Stempak, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/1293496.pdf
    Data publikacji:
    1991
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Laguerre expansions
    generalized twisted convolution
    Riesz
    Cesàro and Abel-Poisson means
    Opis:
    We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions $ℓ_n^a(x) = (n!/Γ(n+a+1))^{1/2} e^{-x/2} L_n^a(x)$, n = 0,1,2,..., in $L^2(ℝ_+, x^adx)$, a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f ∈ L^p(x^adx)$, 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.
    Źródło:
    Studia Mathematica; 1991, 100, 2; 129-147
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On uniqueness of G-measures and g-measures
    Autorzy:
    Hua Fan, Ai
    Powiązania:
    https://bibliotekanauki.pl/articles/1287544.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    G-measures
    g-measures
    ergodic measures
    Riesz products
    quasi-invariance
    dimension of measures
    Opis:
    We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension of Riesz products is calculated.
    Źródło:
    Studia Mathematica; 1996, 119, 3; 255-269
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sur les dimensions de mesures
    Autorzy:
    Hua Fan, Ai
    Powiązania:
    https://bibliotekanauki.pl/articles/1290182.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    upper and lower dimension
    dimension formulas
    unidimensional
    multifractal
    Gibbs measure
    Markov measure
    Riesz product
    Opis:
    Firstly, we introduce the lower and upper dimensions for a measure defined on a metric space. Secondly, we establish the dimension formulas and characterize the unidimensional measures which were introduced by J.-P. Kahane. Lastly, we give some applications of these to the calculus of dimensions and the multifractal analysis of certain well known measures such as Lebesgue measures on Cantor sets, Gibbs measures, Markov measures and Riesz products etc.
    Źródło:
    Studia Mathematica; 1994, 111, 1; 1-17
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Complex Unconditional Metric Approximation Property for $C_{Λ}(\mathbb{T})$ spaces
    Autorzy:
    Li, Daniel
    Powiązania:
    https://bibliotekanauki.pl/articles/1220918.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Unconditional Metric Approximation Property
    translation invariant spaces of continuous functions
    Rosenthal set
    Riesz set
    linear invariant lifting
    Opis:
    We study the Complex Unconditional Metric Approximation Property for translation invariant spaces $C_{Λ}(\mathbb{T})$ of continuous functions on the circle group. We show that although some "tiny" (Sidon) sets do not have this property, there are "big" sets Λ for which $C_{Λ}(\mathbb{T})$ has (ℂ-UMAP); though these sets are such that $L_{Λ}^{∞}(\mathbb{T})$ contains functions which are not continuous, we show that there is a linear invariant lifting from these $L_{Λ}^{∞}(\mathbb{T})$ spaces into the Baire class 1 functions.
    Źródło:
    Studia Mathematica; 1996, 121, 3; 231-247
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Double exponential integrability, Bessel potentials and embedding theorems
    Autorzy:
    Edmunds, David E.
    Gurka, Petr
    Opic, Bohumír
    Powiązania:
    https://bibliotekanauki.pl/articles/1289003.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Bessel potential
    Riesz potential, generalized Lorentz-Zygmund spaces
    exponential integrability
    Hardy inequality
    Orlicz spaces
    Bessel potential spaces
    Opis:
    This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
    Źródło:
    Studia Mathematica; 1995, 115, 2; 151-181
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Measures and lacunary sets
    Autorzy:
    Lefèvre, Pascal
    Powiązania:
    https://bibliotekanauki.pl/articles/1216990.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    stationary sets
    p-Sidon sets
    sets of continuity
    Λ(1) sets
    Riesz sets
    random Fourier series
    (p,q)-summing operators
    Opis:
    We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
    Źródło:
    Studia Mathematica; 1999, 133, 2; 145-161
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vector series whose lacunary subseries converge
    Autorzy:
    Drewnowski, Lech
    Labuda, Iwo
    Powiązania:
    https://bibliotekanauki.pl/articles/1206244.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    subseries convergence
    lacunary subseries
    zero-density subseries
    lacunary convergence property
    topological Riesz space of measurable functions
    topological vector space of Bochner measurable functions
    Lebesgue property
    Levi property
    copy of $c_0$
    Opis:
    The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $∑_n x_n$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $∑_k x_{n_k}$ (i.e. those with $n_{k+1} - n_k → ∞$) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence Property, or ZCP, is defined similarly though of lesser importance here. It is shown that for every ℒ-convergent series the set of all its finite sums is metrically bounded; however, it need not be topologically bounded. Next, a space with the LCP contains no copy of the space $c_0$. The converse holds for Banach spaces and, more generally, sequentially complete locally pseudoconvex spaces. However, an F-lattice of measurable functions is constructed that has both the Lebesgue and Levi properties, and thus contains no copy of $c_0$, and, nonetheless, lacks the LCP. The main (and most difficult) result of the paper is that if a Banach space E contains no copy of $c_0$ and λ is a finite measure, then the Bochner space $L_0$ (λ,e) has the LCP. From this, with the help of some Orlicz-Pettis type theorems proved earlier by the authors, the LCP is deduced for a vast class of spaces of (scalar and vector) measurable functions that have the Lebesgue type property and are "metrically-boundedly sequentially closed" in the containing $L_0$ space. Analogous results about the convergence of ℒ-convergent positive series in topological Riesz spaces are also obtained. Finally, while the LCP implies the ZCP trivially, an example is given that the converse is false, in general.
    Źródło:
    Studia Mathematica; 2000, 138, 1; 53-80
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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