scholarly journals Radial maximal function characterizations for Hardy spaces on RD-spaces

2009 ◽  
Vol 137 (2) ◽  
pp. 225-251 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Radial Maximal Function

scholarly journals Maximal characterisation of local Hardy spaces on locally doubling manifolds

2021 ◽  
Author(s):  
Alessio Martini ◽  
Stefano Meda ◽  
Maria Vallarino
Keyword(s):  
Riemannian Manifold ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Integrable Function ◽  
Local Heat ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Local Hardy Spaces ◽  
Atomic Hardy Space ◽  
Radial Maximal Function

AbstractWe prove a radial maximal function characterisation of the local atomic Hardy space $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama.

scholarly journals REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS

2011 ◽  
Vol 09 (03) ◽  
pp. 345-368 ◽  
Author(s):  
DACHUN YANG ◽  
DONGYONG YANG
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Real Variable ◽  
Bessel Operator ◽  
Bessel Operators ◽  
Lusin Area Function ◽  
Radial Maximal Function ◽  
Nontangential Maximal Function

Let λ > 0, p ∈ ((2λ + 1)/(2λ + 2), 1], and [Formula: see text] be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces Hp((0,∞),dmλ) associated with △λ in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood–Paley g-function and the Lusin-area function, where dmλ(x) ≡ x2λ dx. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.

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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