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.

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.

New Calderón reproducing formulae with exponential decay on spaces of homogeneous type

2019 ◽  
Vol 62 (2) ◽  
pp. 283-350 ◽  
Author(s):  
Ziyi He ◽  
Liguang Liu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Exponential Decay ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

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

The Boundedness of Maximal Functions in Orlicz–Campanato Spaces of Homogeneous Type

2008 ◽  
Vol 15 (2) ◽  
pp. 377-388
Author(s):  
Xiangxing Tao ◽  
Qinqin Chen
Keyword(s):  
Half Space ◽  
Maximal Operator ◽  
Carleson Measure ◽  
Normal Space ◽  
Space Of Homogeneous Type ◽  
Campanato Space ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Doubling Property ◽  
Littlewood Maximal Operator

Abstract Let (𝑋,𝑑,μ) be a normal space of homogeneous type, 𝑋+ be the upper half-space equipped with a Carleson measure β, and let Φ be an N-function and φ a suitable function satisfying the doubling property. We prove that the generalized Hardy–Littlewood maximal operator 𝑀 is bounded from the Orlicz–Campanato space 𝐿Φ,φ (𝑋,μ) to 𝐿Φ,φ (𝑋+,β).

scholarly journals New interpolation theorems related to the space BMOA on spaces of homogeneous type

2006 ◽  
Vol 74 (3) ◽  
pp. 347-358
Author(s):  
Qi-Hui Zhang ◽  
Da-Ping Ni
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Approximation To The Identity

Let (χ, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss, and BMOA(χ) be the space of BMO type associated with an “approximation to the identity” {At}t>0 and introduced by Duong and Yan. In this paper, we establish new interpolation theorems of operators related to the space BMOA(χ).

scholarly journals Notes on boundedness of spectral multipliers on Hardy spaces associated to operators

2011 ◽  
Vol 203 ◽  
pp. 109-122
Author(s):  
Bui The Anh
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Analytic Semigroup ◽  
Adjoint Operator ◽  
Upper Bounds ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Suitable Function

AbstractLetLbe a nonnegative self-adjoint operator onL2(X), whereXis a space of homogeneous type. Assume thatLgenerates an analytic semigroupe–tlwhose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplierF(L) is bounded onfor 0< p< 1, the Hardy space associated to operatorL, whenFis a suitable function.

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