- Publ. Mat.
- Volume 62, Number 2 (2018), 475-535.
Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of $H^1_L(w)$
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  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.
Publ. Mat., Volume 62, Number 2 (2018), 475-535.
Received: 9 January 2017
Revised: 2 February 2017
First available in Project Euclid: 16 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42B30: $H^p$-spaces 35J15: Second-order elliptic equations 42B37: Harmonic analysis and PDE [See also 35-XX] 42B25: Maximal functions, Littlewood-Paley theory 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47G10: Integral operators [See also 45P05]
Hardy spaces second order divergence form elliptic operators heat and Poisson semigroups conical square functions non-tangential maximal functionss molecular decomposition Muckenhoupt weights off-diagonal estimates
Martell, José María; Prisuelos-Arribas, Cruz. Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of $H^1_L(w)$. Publ. Mat. 62 (2018), no. 2, 475--535. doi:10.5565/PUBLMAT6221806. https://projecteuclid.org/euclid.pm/1529114424