论文标题
奇异的整体运营商，$ t1 $定理，利特伍德 - 帕利理论和dunkl设置中的耐力空间
Singular integral operators, $T1$ theorem, Littlewood-Paley theory and Hardy spaces in Dunkl Setting
论文作者
论文摘要
本文的目的是在涉及欧几里得公制和dunkl公制的dunkl设置中引入新的单数积分运算符。然后，我们提供$ t1 $定理，这些运营商的$ l^2 $的有限标准。利用这种奇异的整体操作者理论，我们建立了Littlewood-Paley理论和Dunkl-Hardy空间。作为应用，给出了单数积分运算符的界限，尤其是在Dunkl-Hardy空间上的Dunkl-Rieze变换。 $ l^2 $理论和奇异整体操作员理论扮演着至关重要的角色。 New tools developed in this paper include the weak-type discrete Calderón reproducing formulae, new test functions, and distributions, the Littlewood-Paley, the wavelet-type decomposition, and molecule characterizations of the Dunkl-Hardy space, Coifman's approximation to the identity and the decomposition of the identity operator on $L^2$, Meyer's commutation Lemma, and new almost DUNKL设置中的正交估计。
The purpose of this paper is to introduce a new class of singular integral operators in the Dunkl setting involving both the Euclidean metric and the Dunkl metric. Then we provide the $T1$ theorem, the criterion for the boundedness on $L^2$ for these operators. Applying this singular integral operator theory, we establish the Littlewood-Paley theory and the Dunkl-Hardy spaces. As applications, the boundedness of singular integral operators, particularly, the Dunkl-Rieze transforms, on the Dunkl-Hardy spaces is given. The $L^2$ theory and the singular integral operator theory play crucial roles. New tools developed in this paper include the weak-type discrete Calderón reproducing formulae, new test functions, and distributions, the Littlewood-Paley, the wavelet-type decomposition, and molecule characterizations of the Dunkl-Hardy space, Coifman's approximation to the identity and the decomposition of the identity operator on $L^2$, Meyer's commutation Lemma, and new almost orthogonal estimates in the Dunkl setting.
