Banach Journal of Mathematical Analysis

Tent spaces at endpoints

Yong Ding and Ting Mei

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In 1985, Coifman, Meyer, and Stein gave the duality of the tent spaces; that is, (Tqp(R+n+1))*=Tq'p'(R+n+1) for 1<p,q<, and (T1(R+n+1))*=C(R+n+1), (Tq1(R+n+1))*=Tq'(R+n+1) for 1<q<, where C(R+n+1) denotes the Carleson measure space on R+n+1. We prove that (Cv(R+n+1))*=T1(R+n+1), which we introduced recently, where Cv(R+n+1) is the vanishing Carleson measure space on R+n+1. We also give the characterizations of Tq(R+n+1) by the boundedness of the Poisson integral. As application, we give the boundedness and compactness on Lq(Rn) of the paraproduct πF associated with the tent space Tq(R+n+1), and we extend partially an interesting result given by Coifman, Meyer, and Stein, which establishes a close connection between the tent spaces T2p(R+n+1) (1p) and Lp(Rn), Hp(Rn) and BMO(Rn) spaces.

Article information

Banach J. Math. Anal. Volume 11, Number 4 (2017), 841-863.

Received: 20 June 2016
Accepted: 20 November 2016
First available in Project Euclid: 17 August 2017

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Digital Object Identifier

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

tent space vanishing Carleson measure vanishing tent space Poisson integral paraproduct


Ding, Yong; Mei, Ting. Tent spaces at endpoints. Banach J. Math. Anal. 11 (2017), no. 4, 841--863. doi:10.1215/17358787-2017-0020.

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