Open Access
October 2017 Tent spaces at endpoints
Yong Ding, Ting Mei
Banach J. Math. Anal. 11(4): 841-863 (October 2017). DOI: 10.1215/17358787-2017-0020


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.


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Yong Ding. Ting Mei. "Tent spaces at endpoints." Banach J. Math. Anal. 11 (4) 841 - 863, October 2017.


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

zbMATH: 1385.42022
MathSciNet: MR3708532
Digital Object Identifier: 10.1215/17358787-2017-0020

Primary: 42B35
Secondary: 42B99

Keywords: paraproduct , Poisson integral , ‎tent space , vanishing Carleson measure , vanishing tent space

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 4 • October 2017
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