scholarly journals Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates

2016 ◽  
Vol 141 ◽  
pp. 16-42 ◽  
Author(s):  
Ciqiang Zhuo ◽  
Dachun Yang
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Adjoint Operators ◽  
Gaussian Estimates

scholarly journals Local Hardy Spaces with Variable Exponents Associated with Non-negative Self-Adjoint Operators Satisfying Gaussian Estimates

2019 ◽  
Vol 30 (3) ◽  
pp. 3275-3330 ◽  
Author(s):  
Víctor Almeida ◽  
Jorge J. Betancor ◽  
Estefanía Dalmasso ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Local Hardy Spaces ◽  
Adjoint Operators ◽  
Gaussian Estimates

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

scholarly journals Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators

2016 ◽  
Vol 28 (5) ◽  
pp. 823-856 ◽  
Author(s):  
Jun Cao ◽  
Svitlana Mayboroda ◽  
Dachun Yang
Keyword(s):  
Elliptic Operator ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Divergence Form ◽  
Higher Order ◽  
Square Functions ◽  
Maximal Interval ◽  
Measurable Coefficients ◽  
Order Elliptic Operator ◽  
Higher Order Elliptic Operator

AbstractLet L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and ${(p_{-}(L),p_{+}(L))}$ be the maximal interval of exponents ${q\in[1,\infty]}$ such that the semigroup ${\{e^{-tL}\}_{t>0}}$ is bounded on ${L^{q}(\mathbb{R}^{n})}$. In this article, the authors establish the non-tangential maximal function characterizations of the associated Hardy spaces ${H_{L}^{p}(\mathbb{R}^{n})}$ for all ${p\in(0,p_{+}(L))}$, which when ${p=1}$, answers a question asked by Deng, Ding and Yao in [21]. Moreover, the authors characterize ${H_{L}^{p}(\mathbb{R}^{n})}$ via various versions of square functions and Lusin-area functions associated to the operator L.

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