Convergence and Stability of the Calderón Reproducing Formula in H1 and BMO
Convergence and Stability of the Calderón Reproducing Formula in H1 and BMO
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DOI：
10.1007/s00041-010-9165-y
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发表时间：
2011-01
影响因子：
1.2
通讯作者：
Michael Wilson
中科院分区：
文献类型：
--
作者：
Michael Wilson
本文证明了Calderón再生公式的一般形式收敛于H 1（Rd）（February man和Stein的真实的哈代空间）作为逼近积分的自然极限.我们证明了这种收敛是H1-稳定的关于小误差的伸缩和平移。利用对偶性，我们证明了Calderón再生公式收敛，在一个稳定的方式，弱-BMO。我们给出了公式的稳定性和收敛速度的定量估计。这些定理推广了作者关于Calderón再生公式在Lp（w）中的收敛性和稳定性的结果，其中1<p<∞且为MuckenhouptAp-weight.
We prove that a general form of the Calderón reproducing formula converges inH1(Rd) (the real Hardy space of Fefferman and Stein) as a natural limit of approximating integrals. We show that this convergence isH1-stable with respect to small errors in dilation and translation. Using duality, we show that the Calderón reproducing formula converges, in a stable fashion, weak-∗ inBMO. We give quantitative estimates of the formula’s stability and rate of convergence. These theorems generalize results of the author on the convergence and stability of the Calderón reproducing formula inLp(w), where 1<p<∞ andwis a MuckenhouptApweight.