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October 2019 Variable Hardy–Lorentz spaces associated to operators satisfying Davies–Gaffney estimates
Yahui Zuo, Khedoudj Saibi, Yong Jiao
Banach J. Math. Anal. 13(4): 769-797 (October 2019). DOI: 10.1215/17358787-2018-0035

Abstract

Let L be a one-to-one operator of type w with w[0,π/2), which satisfies the Davies–Gaffney estimates and has a bounded holomorphic calculus, and let p() be a measurable function on Rn with 0<p:=essinf xRnp(x)esssup xRnp(x)=:p+<. Under the assumption that p() satisfies the global log-Hölder condition, we introduce the variable Hardy–Lorentz space HLp(),q(Rn) for 0<q< and construct its molecular decomposition. Furthermore, we investigate the dual spaces of the variable Hardy–Lorentz space HLp(),q(Rn) with 0<pp+1 and 0<q<. These results are new even when p() is a constant.

Citation

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Yahui Zuo. Khedoudj Saibi. Yong Jiao. "Variable Hardy–Lorentz spaces associated to operators satisfying Davies–Gaffney estimates." Banach J. Math. Anal. 13 (4) 769 - 797, October 2019. https://doi.org/10.1215/17358787-2018-0035

Information

Received: 14 June 2018; Accepted: 26 October 2018; Published: October 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07118762
MathSciNet: MR4016897
Digital Object Identifier: 10.1215/17358787-2018-0035

Subjects:
Primary: 42B30
Secondary: 42B25, 42B35

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 4 • October 2019
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