scholarly journals Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications

2020 ◽  
Vol 278 (8) ◽  
pp. 108423 ◽  
Author(s):  
The Anh Bui ◽  
Xuan Thinh Duong ◽  
Fu Ken Ly
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Finite Measure ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

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.

scholarly journals A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type

2018 ◽  
Vol 25 (5) ◽  
pp. 2197-2267 ◽  
Author(s):  
Ziyi He ◽  
Yongsheng Han ◽  
Ji Li ◽  
Liguang Liu ◽  
Dachun Yang ◽  
...  
Keyword(s):  
Hardy Spaces ◽  
Real Variable ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Variable Theory

scholarly journals Boundedness of Some Paraproducts on Spaces of Homogeneous Type

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2591
Author(s):  
Xing Fu
Keyword(s):  
Exponential Decay ◽  
Hardy Spaces ◽  
Summation Formula ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Doubling Condition ◽  
J 13 ◽  
Abel Summation

Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the author develops a partial theory of paraproducts {Πj}j=13 defined via approximations of the identity with exponential decay (and integration 1), which are extensions of paraproducts defined via regular wavelets. Precisely, the author first obtains the boundedness of Π3 on Hardy spaces and then, via the methods of interpolation and the well-known T(1) theorem, establishes the endpoint estimates for {Πj}j=13. The main novelty of this paper is the application of the Abel summation formula to the establishment of some relations among the boundedness of {Πj}j=13, which has independent interests. It is also remarked that, throughout this article, μ is not assumed to satisfy the reverse doubling condition.

scholarly journals vector-valued singular integrals and maximal functions on spaces of homogeneous type

2009 ◽  
Vol 104 (2) ◽  
pp. 296 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Maximal Functions ◽  
Integral Theory ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Vector Valued

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.

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