Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus

Duong, Xuan Thinh; Li, Ji

doi:10.1016/j.jfa.2013.01.006

Cited by 93 publications

(76 citation statements)

References 17 publications

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“…For the second direction (in generalizing the Laplacian to some other operator L) we cite the body of work in [13,12,14,15,16,19,25,26,27]. The starting point here is to replace the semigroup e −t 2 ∆ in (i) and (ii) by some other semigroup e −t 2 L , but one can define an adaptation of (iii) by encoding the cancellation of atoms using L in a certain way (see [25] and also Definition 2.1 below).…”

Section: Introductionmentioning

confidence: 99%

“…More precisely we replace the role of 1 in the definitions of the spaces in (3) and (4) by a positive function ρ(x) (which we call a 'critical radius function') that does not fluctuate too quickly in a certain sense (see (12)). Spaces induced by such a function ρ arise as spaces related to lower order perturbations of L. A model case is the Schrödinger operator −∆ + V where one has H p −∆+V, rad (X) = h p at,ρ (X) (5) for certain potentials V and with ρ related to V .…”

Section: Introductionmentioning

confidence: 99%

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Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type

Duong

2018

Trans. Amer. Math. Soc.

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Abstract. Let X be a space of homogeneous type and let L be a nonnegative self-adjoint operator on L 2 (X) enjoying Gaussian estimates. The main aim of this paper is twofold. Firstly, we prove (local) nontangential and radial maximal function characterizations for the local Hardy spaces associated to L. This gives the maximal function characterization for local Hardy spaces in the sense of Coifman and Weiss provided that L satisfies certain extra conditions. Secondly we introduce local Hardy spaces associated with a critical function ρ which are motivated by the theory of Hardy spaces related to Schrödinger operators and of which include the local Hardy spaces of Coifman and Weiss as a special case. We then prove that these local Hardy spaces can be characterized by (local) nontangential and radial maximal functions related to L and ρ, and by global maximal functions associated to 'perturbations' of L. We apply our theory to obtain a number of new results on maximal characterizations for the local Hardy type spaces in various settings ranging from Schrödinger operators on manifolds to Schrödinger operators on connected and simply connected nilpotent Lie groups.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type

Duong

2018

Trans. Amer. Math. Soc.

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“…For the theory of Hardy spaces associated to operators, it has attracted a lot of attention in the last decades, and has been a very active research topic in harmonic analysis -see for example, [1,2,3,7,10,11,12,13,15,16,17,18,21,23,24].…”

Section: Introductionmentioning

confidence: 99%

“…We now recall the notion of a (p, q, M)-atom associated to an operator L ( [2,11,15]). The atomic Hardy space H p L,at,q,M (X) is defined as follows.…”

Section: Introductionmentioning

confidence: 99%

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Maximal function characterizations for Hardy spaces associated with nonnegative self-adjoint operators on spaces of homogeneous type

Song

Yan

2017

J. Evol. Equ.

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Abstract. Let X be a metric measure space with a doubling measure and L be a nonnegative selfadjoint operator acting on L 2 (X). Assume that L generates an analytic semigroup e −tL whose kernels p t (x, y) satisfy Gaussian upper bounds but without any assumptions on the regularity of space variables x and y. In this article we continue a study in [21] to give an atomic decomposition for the Hardy spaces H p L,max (X) in terms of the nontangential maximal function associated with the heat semigroup of L, and hence we establish characterizations of Hardy spaces associated to an operator L, via an atomic decomposition or the nontangential maximal function. We also obtain an equivalence of H p L,max (X) in terms of the radial maximal function.

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Real-variable characterizations of Musielak-Orlicz-Hardy spaces associated with Schrödinger operators on domains

Chang

Yang

et al. 2015

Math. Meth. Appl. Sci.

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Communicated by P. SacksLet n 3, be a strongly Lipschitz domain of R n and L :D C V a Schrödinger operator on L 2 . / with the Dirichlet boundary condition, where is the Laplace operator and the nonnegative potential V belongs to the reverse Hölder class RH q0 .R n / for some q 0 > n=2. Assume that the growth function ' : . / with p 2 .n=.n C ı/, 1 (in this case, '.x, t/ :D t p for all x 2 and t 2 OE0, 1/).

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Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus

Cited by 93 publications

References 17 publications

Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type

Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type

Maximal function characterizations for Hardy spaces associated with nonnegative self-adjoint operators on spaces of homogeneous type

Real-variable characterizations of Musielak-Orlicz-Hardy spaces associated with Schrödinger operators on domains

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