Criterion of the boundedness of singular integrals on spaces of homogeneous type
Criterion of the boundedness of singular integrals on spaces of homogeneous type
复制标题
齐次类型空间上奇异积分的有界性判据
DOI：
10.1016/j.jfa.2016.09.006
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发表时间：
2015-12
影响因子：
1.7
通讯作者：
Li Ji
中科院分区：
文献类型：
--
作者：
Han Yanchang;Han Yongsheng;Li Ji
众所周知，几何因素在调和分析的许多问题中起着决定性的作用。本文的主要目的是给出Hardy空间及其对偶上奇异积分的有界性判据，特别是Coifman和Weiss意义上齐次型（X, d, μ）空间的BMO，其中拟度量d可能没有正则性，而度量μ只满足倍性。我们没有对拟度规和加倍测度作任何额外的几何假设，因此，本文的结果推广到以前所有有关的关于拟度规d和测度μ的额外几何假设的全部一般性。为了实现我们的目标，我们证明了Coifman和Weiss引入的原子Hardy空间与用小波系数定义的Hardy空间是一致的，并为这种一般情况发展了分子理论。本文使用的主要工具是原子分解，最近由Auscher和Hytönen构造的正交小波基，离散的Calderón-type再现公式，几乎正交估计，实现各种停止时间参数以及Hardy空间与Carleson测度空间的对偶性。
It was well known that geometric considerations enter in a decisive way in many questions of harmonic analysis. The main purpose of this paper is to provide the criterion of the boundedness for singular integrals on the Hardy spaces and as well as on its dual, particularly on BMO for spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property. We make no additional geometric assumptions on the quasi-metric or the doubling measure and thus, the results of this paper extend to the full generality of all related previous ones, in which the extra geometric assumptions were made on both the quasi-metric d and the measure μ. To achieve our goal, we prove that the atomic Hardy spaces introduced by Coifman and Weiss coincide with the Hardy spaces defined in terms of wavelet coefficients and develop the molecule theory for this general setting. The main tools used in this paper are atomic decomposition, the orthonormal wavelet basis constructed recently by Auscher and Hytönen, the discrete Calderón-type reproducing formula, the almost orthogonal estimates, implement various stopping time arguments and the duality of the Hardy spaces with the Carleson measure spaces.
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DOI：
10.1007/978-3-540-88745-4
发表时间：
2008-12
期刊：
--
影响因子：
--
作者：
D. Deng;Yongsheng Han;Y. Meyer
通讯作者：
D. Deng;Yongsheng Han;Y. Meyer
影响因子：
1.7
作者：
R. Macías;C. Segovia
通讯作者：
R. Macías;C. Segovia
影响因子：
1.7
作者：
R. Macías;C. Segovia
通讯作者：
R. Macías;C. Segovia
影响因子：
1.7
作者：
Michael Frazier;B. Jawerth
通讯作者：
Michael Frazier;B. Jawerth
DOI：
10.1090/s0002-9904-1977-14325-5
发表时间：
1977-01-01
影响因子：
1.3
作者：
COIFMAN, RR;WEISS, G
通讯作者：
WEISS, G