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卷积型Calder\'{o}n-Zygmund算子的新算法 总被引:1,自引:0,他引:1
Beylkin-Coifman-Rokhlin
(B-C-R)算法表明算子通常可用$2n$维小波来分析, 而本文用
基于$n$维小波来引入一种新方法考虑卷积型 Calder\'{o}n-Zygmund
(C-Z)算子. 利用此方法来研究算子的逼近, 此逼近算法不仅比 B-C-R
算法简单而且有更快的逼近速度. 还证明了 H\"{o}rmander
条件能够保证算子在 Besov 空间$\dot{B}_p^{0,q}\ (1\leq p,\, q
\leq\infty)$ 和 Triebel--Lizorkin 空间$\dot{F}_p^{0,q}(1
相似文献
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杨占英 《数学物理学报(B辑英文版)》2010,(4):1338-1346
In this article, the author introduces a class of non-convolution Calder′on-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces ■p0 ,q(1 ≤p,q ≤∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hrmander condition can ensure the boundedness of convolution-type Calder′on-Zygmund operators on Besov spaces ■p0 ,q(1 ≤p,q ≤∞). However, the proof is quite different from the previous one. 相似文献
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本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理. 相似文献
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In this paper, we study a class of hyperbolic-parabolic problems in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes. We focus on the homogenization of these equations, which generalizes those achieved by BensoussanLions-Papanicolau and Migorski. The proof is based on the periodic unfolding method in perforated domains. 相似文献
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For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q (1 〈 p,q 〈 ∞) and on a party of endpoint spaces FO,q (1 ≤ q ≤ 2), hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q (2 〈 q ≤ ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q (2 〈 q ≤ ∞) under an integrable condition which approaches HSrmander condition infinitely. 相似文献
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This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q(2 q ≤ ∞) under a very weak pointwise regularity condition. 相似文献
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