## Taiwanese Journal of Mathematics

### A Class of $\alpha$-Carleson Measures

#### Abstract

In the present paper, we introduce a class of $\alpha$-Carleson measures $\mathcal{C}_{\alpha,v}(\mathbb{R}^{n+1}_+)$, which is called by the vanishing $\alpha$-Carleson measures. We prove that $\mathcal{C}_{1/p,v}(\mathbb{R}^{n+1}_+)$ is just a predual of the tent space $\widetilde{T}_{\infty}^p$ ($0 \lt p \lt 1$). Furthermore, we construct the $\alpha$-Carleson measures and the vanishing $\alpha$-Carleson measures by the Campanato functions and its a subclass, respectively. Moreover, a characterization of the vanishing $\alpha$-Carleson measure by the compactness of Poisson integral is given in this paper. Finally, as some applications, we give the $(L^{2/\alpha},L^2)$ boundedness and compactness for some paraproduct operators.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 5 (2018), 1217-1243.

Dates
Accepted: 21 November 2017
First available in Project Euclid: 16 December 2017

https://projecteuclid.org/euclid.twjm/1513393253

Digital Object Identifier
doi:10.11650/tjm/171103

Mathematical Reviews number (MathSciNet)
MR3859373

Zentralblatt MATH identifier
06965416

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 42B99: None of the above, but in this section

#### Citation

Mei, Ting; Ding, Yong. A Class of $\alpha$-Carleson Measures. Taiwanese J. Math. 22 (2018), no. 5, 1217--1243. doi:10.11650/tjm/171103. https://projecteuclid.org/euclid.twjm/1513393253

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