共查询到20条相似文献,搜索用时 15 毫秒
1.
研究D-C chang等人引进的五个区域Hardy空间,刻划这些空间的原子分解和对偶空间,揭示了这些空间的内在联系。 相似文献
2.
In this article we are interested in conditions on the coefficients of a Walsh multiplier operator that imply the operator is bounded on certain dyadic Hardy spaces H p , 0 < p < ∞. In particular, we consider two classical coefficient conditions, originally introduced for the trigonometric case, the Marcinkiewicz and the Hörmander–Mihlin conditions. They are known to be sufficient in the spaces L p , 1 < p < ∞. Here we study the corresponding problem on dyadic Hardy spaces, and find the values of p for which these conditions are sufficient. Then, we consider the cases of H 1 and L 1 which are of special interest. Finally, based on a recent integrability condition for Walsh series, a new condition is provided that implies that the multiplier operator is bounded from L 1 to L 1, and from H 1 to H 1. We note that existing multiplier theorems for Hardy spaces give growth conditions on the dyadic blocks of the Walsh series of the kernel, but these growth are not computable directly in terms of the coefficients. 相似文献
3.
Yasuo Komori 《Acta Mathematica Hungarica》2002,95(1-2):21-27
We show the atomic decomposition of molecule on discrete Hardy spaces without using the theory of continuous Hardy spaces 相似文献
4.
New Hardy Spaces Associated with Herz Spaces and Beurling Algebras on Homogeneous Groups 总被引:3,自引:0,他引:3
Yin Sheng Jiang 《数学学报(英文版)》2002,18(4):661-670
The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and
establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy
spaces and the boundedness of the central δ-Calderón-Zygmund operators on these Hardy spaces are studied.
Received January 13, 2000, Accepted July 26, 2000 相似文献
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6.
Hardy's inequalities are proved for higher-dimensional Hermite and special Hermite expansions of functions in Hardy spaces. Inequalities for multiple Laguerre expansions are also deduced.
7.
A pair of dual frames with almost exponentially localized elements (needlets) are constructed on based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients. 相似文献
8.
In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the Hardy type spaces X k (M), introduced in a previous paper of the authors, have an atomic characterization. An atom in X k (M) is an atom in the Hardy space H 1(M) introduced by Carbonaro, Mauceri, and Meda, satisfying an ??infinite dimensional?? cancellation condition. As an application, we prove that the Riesz transforms of even order $\nabla^{2k} \mathcal{L}^{-k}$ map X k (M) into L 1(T 2k M). 相似文献
9.
罗罗 《数学物理学报(A辑)》2007,27(2):204-207
作者研究了CN 中单位球B上不同Hardy空间之间的乘法算子, 给出了有界的乘法算子Mg: Hp(B) → Hq(B)$的特征. 相似文献
10.
本文延拓Fefferman-Stein加权极大不等式到齐次群上,作为其应用,建立了齐次群上伴随于Herz空间和Beurling代数的Hardy空间极大特征。同时,得到了具(α,r)型核的卷积算子在这些Hardy空间上的有界性。 相似文献
11.
J. Hounie Rafael Augusto dos Santos Kapp 《Journal of Fourier Analysis and Applications》2009,15(2):153-178
In this work, we study the continuity of pseudodifferential operators on local Hardy spaces h
p
(ℝ
n
) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S
1,δ
0(ℝ
n
), 0≤δ<1, and in some subclasses of S
1,10(ℝ
n
) are bounded on h
p
(ℝ
n
) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂
t
+ib(x,t)∂
x
, b(x,t)≥0, in spaces of mixed norm involving Hardy spaces.
Work supported in part by CNPq, FINEP, and FAPESP. 相似文献
12.
Discrete Littlewood-Paley-Stein Characterization and L 2 Atomic Decomposition of Local Hardy Spaces 下载免费PDF全文
Usually, the condition that T is bounded on L2(ℝn) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)= ∑i λiT(ai), provided that f = ∑i λiai in L2 (ℝn), where ai is an L2 atom of this Hardy space. So far, the L2 atomic decomposition of local Hardy spaces hp(ℝn), 0 > p ≤ 1, hasn’t been established. In this paper, we will solve this problem, and also show that hp(ℝn) can also be characterized by discrete Littlewood-Paley functions. 相似文献
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14.
Anatoly Ryabogin Dmitry Ryabogin 《Proceedings of the American Mathematical Society》2007,135(8):2461-2470
In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to for all .
15.
In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels. 相似文献
16.
Continuity of Higher Order Commutators on Certain Hardy Spaces 总被引:12,自引:0,他引:12
In this paper, the autors study the continuity properties of higher order commutators generated by the homogeneous fractional
integral and BMO functions on certain Hardy spaces, weak Hardy spaces and Herz-type Hardy spaces.
Received October 13, 2000, Accepted November 29, 2001 相似文献
17.
本文通过建立与特殊Hermite展开相对应的Littlewood-Paley分解和相关的扭曲卷积核的L2估计,得到特殊Hermite展开的乘子定理,作为该结果的应用,给出了Hermite函数及Laguerre函数展开的乘子定理。 相似文献
18.
We establish the connection between the boundedness of convolution operators on Hp(ℝN) and some related operators on Hp(ℤN). The results we obtain here extend the already known for Lp spaces with p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential type belonging to Hardy spaces 相似文献
19.
本文证明了弱Hardy正规鞅空间wHp和wH^sp上的原子分解定理.利用鞅的原子分解给出了弱Hardy正规鞅空间上的次线性算子有界的一个充分条件.利用这个条件得到了关于正规鞅的一些弱Lp范数不等式和弱(p,p)型不等式.这些结果是经典Hp鞅论中一些重要结果的弱型对应. 相似文献
20.
A Note on Certain Block Spaces on the Unit Sphere 总被引:1,自引:0,他引:1
Xiao Feng YE Xiang Rong ZHU 《数学学报(英文版)》2006,22(6):1843-1846
In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1(S^n-1)+L(ln+L)^1+v(s^n-1),v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq^0.v(S^n-1)are proper subspaces of H1 (S^n- 1), 相似文献