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1.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
2.
Yinsheng Jiang Lin Tang 《分析论及其应用》2005,21(4):301-310
In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKα,p q(G) and HKq,p q(G), where 1 < q <∞, Q(1 - 1/q) ≤α<∞, 0 < p <∞ and G denotes a graded homogeneous Lie group. 相似文献
3.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
4.
A. S. Romanyuk 《Ukrainian Mathematical Journal》2009,61(4):613-626
Exact-order estimates are obtained for the best orthogonal trigonometric approximations of the Besov (B
p,θ
r
) and Nukol’skii (H
p
r
) classes of periodic functions of many variables in the metric of L
q
, 1 ≤ p, q ≤ ∞. We also establish the orders of the best approximations of functions from the same classes in the spaces L
1 and L
∞ by trigonometric polynomials with the corresponding spectrum. 相似文献
5.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
6.
Bruno De Malafosse Eberhard Malkowsky 《Rendiconti del Circolo Matematico di Palermo》2002,51(2):277-294
We give here some properties of the sets
α(uΔ) generalizing the space of generalized difference sequencesl
∞(uΔ). Then we study spaces related to the sets of sequences that are strongly convergent or strongly bounded. Next we define
from the sets of spaces that are (N,q) summable or bounded the sets of spaces that are (N,q)α-bounded orr-bounded. Then we give some properties of these spaces using Banach space of the forms
α. 相似文献
7.
M. Felten 《Acta Mathematica Hungarica》2008,118(3):227-263
Lubinsky and Totik’s decomposition [11] of the Cesàro operators σ
n
(α,β)
of Jacobi expansions is modified to prove uniform boundedness in weighted sup norms, i.e., ‖w
(a,b)
σ
n
(α,β)
‖∞ ≦ C‖w
(a,b)
f‖∞, whenever α,β ≧ −1/2 and a, b are within the square around (α/2 + 1/4, α/2 + 1/4) having a side length of 1. This approach uses only classical results from the theory of orthogonal polynomials and
various estimates for the Jacobi weights. The present paper is concerned with the main theorems and ideas, while a second
paper [7] provides some necessary estimations.
相似文献
8.
HuangZhenyu 《高校应用数学学报(英文版)》2000,15(1):73-77
Abstract. Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces,the Ishikawa iteration 相似文献
9.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2000,6(4):389-401
The two-parameter dyadic martingale Hardy spacesH
p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series
is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H
1
#
, L1), where the Hardy space H
1
#
is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H
1
#
converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too. 相似文献
10.
As is well known the kernel of the orthogonal projector onto the polynomials of
degree n in L2(wα,β, [−1, 1]), wα,β(t) = (1 − t)α(1 + t)β, can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling
a compactly supported C∞ function then the resulting function has nearly exponential (faster than any polynomial) rate of decay away from the main
diagonal. This result is used for the construction of tight polynomial frames for L2(wα,β) with elements having almost exponential localization. 相似文献
11.
Evgeniy Pustylnik 《Journal d'Analyse Mathématique》1999,79(1):113-157
The Lorentz-Zygmund spaces, introduced by C. Bennett and K. Rudnick in [BR], are generalized by taking the exterior norm in
arbitrary rearrangement invariant spaceE instead of onlyL
r-spaces. On the spacesL
p,α,E thus obtained, we study all operatorsT of two weak types (a, b) and (p, q) with 1≤a<p≤∞, 1≤b<q≤∞, and prove thatT:L
p,α,E→L
q,α−1,E. Moreover, for any set of parametersp, q, α, E, we construct the smallest possible spaceB
q,α,E such thatT:L
p,α,E→B
q,α,E and the largest possible spaceA
p,α,E such thatT:A
p,α,E→L
q,α−1,E. For spaces of all three types, we find their fundamental functions and Boyd indices, state various embeddings, equivalences
and other properties.
The research was supported by the Center of Scientific Absorption of the Ministry of Absorption of the State of Israel. 相似文献
12.
A. S. Fedorenko 《Ukrainian Mathematical Journal》1999,51(12):1945-1949
We obtain estimates exact in order for the best trigonometric and orthogonal trigonometric approximations of the classesL Ψβ,ρ of functions of one variable in the spaceL q in the case 2<p <q < ∞. 相似文献
13.
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (H
p,q
(φ1), H
u,v
(φ2)) for the values of p, q, u, v in three cases: (i) 0 < p ≤ u ≤ ∞, 0 < q ≤ min(1, v) ≤ ∞. (ii) v = ∞, 0 < p ≤ u ≤ ∞, 1 ≤ u, q ≤ ∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤ ∞, and 0 < p ≤ u ≤ ∞ or 1 ≤ p, u ≤ ∞. The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly
the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
14.
In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces
and
, where ω1,ω3 ∈ A1-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study
the boundedness of some potential operators on these spaces.
Supported by the NNSF of China 相似文献
15.
Abstract In this paper, we study Triebel-Lizorkin space estimates for an oscillating multiplier mΩ,α,β. This operator was initially studied by Wainger and by Fefferman-Stein in the Lebesgue spaces. We obtain the boundedness results on the Triebel-Lizorkin space Fpα,q(R^n) for different p, q. 相似文献
16.
It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p
n}, 1≦p
n<∞,p
n→p, the spaceX=(Σ⊕l
p
n)
q
(resp.U=(Σ⊕L
p
n(0, 1))
q
) is uniformly homeomorphic toX⊕l
p (resp.U⊕L
p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent. 相似文献
17.
S. S. Ghazaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(6):329-333
It is proved that the systems of functions {sin(n−β
x}
n=1∞ and {cos(n−β
x}
n=1∞ are not unconditional bases in the spaces L
p
(0, π), p≠ 2. 相似文献
18.
We consider a class of fourth-order nonlinear difference equations of the form {fx006-01} where α, β are ratios of odd positive integers and {p
n}, {q
n} are positive real sequences defined for all n ∈ ℕ(n
0). We establish necessary and sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic
behavior under suitable combinations of convergence or divergence conditions for the sums {fx006-02}.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 8–27, January, 2008. 相似文献
19.
Lattice-universal Orlicz function spacesL
F
α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL
F
α,β[0, 1] with indices α and β such that every Orlicz function spaceL
G
[0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL
F
α,β[0, 1]. The existence of classes of universal Orlicz spacesl
Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case.
Partially supported by BFM2001-1284. 相似文献
20.
Zhanying Yang 《Acta Appl Math》2011,114(3):193-205
In this paper, we are concerned with the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin
spaces. We establish the boundedness on [(F)\dot]10,q\dot{F}_{1}^{0,q} (2<q<∞) under a very weak pointwise regularity condition. The boundedness is established by the Daubechies wavelets and the atomic-molecular
approach. 相似文献