Lp theory for outer measures and two themes of Lennart Carleson united-猫眼课题宝

外测度的 Lp 理论与 Lennart Carleson 的两个主题相结合

DOI：

10.1090/s0273-0979-2014-01474-0

发表时间：

2015

期刊：

arXiv: Classical Analysis and ODEs

影响因子：

通讯作者：

中科院分区：

文献类型：

作者：

C. Thiele

我们发展了一种基于由不同集合的覆盖所产生的外部测度的空间理论。作为特例，该理论包括关于欧几里得空间的经典理论以及先前考虑的一些推广。该理论是描述奇异积分理论方面的框架，如Carleson嵌入定理，副积估计和定理。它对奇异积分理论在时频分析中的推广特别有用，后者起源于Carleson对傅里叶级数收敛性的研究。我们构造并证明了一个广义Carleson嵌入定理，并给出了双线性Hilbert变换的最基本估计到这个新的Carleson嵌入定理的一个相对简短的化简。参考文献

We develop a theory ofspaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classicaltheory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, andtheorems. It is particularly useful for generalizations of singular integral theory in time-frequency analysis, the latter originating in Carleson’s investigation of convergence of Fourier series. We formulate and prove a generalized Carleson embedding theorem and give a relatively short reduction of the most basicestimates for the bilinear Hilbert transform to this new Carleson embedding theorem. References

On Calderón's conjecture for the bilinear Hilbert transform.