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2018 Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of $H^1_L(w)$
José María Martell, Cruz Prisuelos-Arribas
Publ. Mat. 62(2): 475-535 (2018). DOI: 10.5565/PUBLMAT6221806


Given a Muckenhoupt weight $w$ and a second order divergence form elliptic operator $L$, we consider different versions of the weighted Hardy space $H^1_L(w)$ defined by conical square functions and non-tangential maximal functions associated with the heat and Poisson semigroups generated by $L$. We show that all of them are isomorphic and also that $H^1_L(w)$ admits a molecular characterization. One of the advantages of our methods is that our assumptions extend naturally the unweighted theory developed by S. Hofmann and S. Mayboroda in [19] and we can immediately recover the unweighted case. Some of our tools consist in establishing weighted norm inequalities for the non-tangential maximal functions, as well as comparing them with some conical square functions in weighted Lebesgue spaces.


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José María Martell. Cruz Prisuelos-Arribas. "Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of $H^1_L(w)$." Publ. Mat. 62 (2) 475 - 535, 2018.


Received: 9 January 2017; Revised: 2 February 2017; Published: 2018
First available in Project Euclid: 16 June 2018

zbMATH: 06918955
MathSciNet: MR3815287
Digital Object Identifier: 10.5565/PUBLMAT6221806

Primary: 35J15 , 42B25 , 42B30 , 42B37 , 47D06 , 47G10

Keywords: conical square functions , Hardy spaces , heat and Poisson semigroups , molecular decomposition , Muckenhoupt weights , non-tangential maximal functionss , off-diagonal estimates , second order divergence form elliptic operators

Rights: Copyright © 2018 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.62 • No. 2 • 2018
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