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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
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
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
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:
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
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
Tytuł:
Shaking during ion-atom collisions
Autorzy:
Sharma, P.
Nandi, T.
Powiązania:
https://bibliotekanauki.pl/articles/1158707.pdf
Data publikacji:
2016-09
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
31.15.xp
34.50.Fa
25.70.Bc
Opis:
The shaking (shakeup and shakeoff) processes accompanying ion-atom collisions are studied using non-relativistic hydrogenic wave functions for the K-, L- and M-shell electrons in the sudden approximation limit. The role of recoil amplitude in the shaking processes is discussed. It is found that the suddenness of collision between projectile and target nuclei plays a more definitive factor in the shaking of the respective atomic system than the recoil of nuclei.
Źródło:
Acta Physica Polonica A; 2016, 130, 3; 697-700
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Electron elastic collisions with C3F6 molecule
Autorzy:
Możejko, P.
Szmytkowski, Cz.
Powiązania:
https://bibliotekanauki.pl/articles/1954668.pdf
Data publikacji:
2003
Wydawca:
Politechnika Gdańska
Tematy:
electron scattering
elastic cross section
hexafluoropropene
independent atom method
Opis:
We report calculations of differential and integral cross sections for intermediate- and high-energy (50-1000eV) elastic collisions of electrons with hexafluoropropene (C3F6) molecules. The calculations have been carried out using the independent atom model with static-polarization model potential. The present results are compared with elastic cross sections estimated from total and ionization experiments. Agreement between present calculations and the "experiment" is good for energies above 70eV.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2003, 7, 2; 171-178
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Theoretical Study of Energy Levels and Transition Probabilities of Boron Atom
Autorzy:
Tian-yi, Zhang
Neng-wu, Zheng
Powiązania:
https://bibliotekanauki.pl/articles/1807769.pdf
Data publikacji:
2009-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
01.55.+b
31.15.-p
Opis:
Though the electrons configuration for boron atom is simple and boron atom has long been of interest for many researchers, the theoretical studies for properties of BI are not systematic, there are only few results reported on energy levels of high excited states of boron, and transition measurements are generally restricted to transitions involving ground states and low excited states without considering fine structure effects, provided only multiplet results, values for transitions between high excited states are seldom performed. In this article, by using the scheme of the weakest bound electron potential model theory calculations for energy levels of five series are performed and with the same method we give the transition probabilities between excited states with considering fine structure effects. The comprehensive set of calculations attempted in this paper could be of some value to workers in the field because of the lack of published calculations for the BI systems. The perturbations coming from foreign perturbers are taken into account in studying the energy levels. Good agreement between our results and the accepted values taken from NIST has been obtained. We also reported some values of energy levels and transition probabilities not existing on the NIST data bases.
Źródło:
Acta Physica Polonica A; 2009, 116, 2; 141-153
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Temperature of a Single Mn Atom in a CdTe Quantum Dot
Autorzy:
Papierska, J.
Goryca, M.
Wojnar, P.
Kossacki, P.
Powiązania:
https://bibliotekanauki.pl/articles/1791341.pdf
Data publikacji:
2009-11
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
78.67.Hc
71.70.Gm
78.55.Et
75.75.-c
Opis:
In this work we present a study of the temperature of the single magnetic atom embedded in a semiconductor quantum dot versus excitation power and magnetic field. This temperature is defined by the thermal distribution of spin states of single Mn ion, and results from its interaction with the neighborhood. This temperature was found to be much higher than the temperature of the thermal bath. Its dependence on the excitation power and magnetic field is discussed.
Źródło:
Acta Physica Polonica A; 2009, 116, 5; 899-900
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
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