scholarly journals Some Rearrangement Inequalities on Space of Homogeneous Type

2014 ◽  
Vol 04 (09) ◽  
pp. 447-450
Author(s):  
Tiejun Chen
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Rearrangement Inequalities

scholarly journals Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

2016 ◽  
Vol 27 (1) ◽  
pp. 95-119 ◽  
Author(s):  
Theresa C. Anderson ◽  
Tuomas Hytönen ◽  
Olli Tapiola
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Reverse Hölder

scholarly journals A Variant of the Notion of a Space of Homogeneous Type

1995 ◽  
Vol 132 (1) ◽  
pp. 119-140 ◽  
Author(s):  
A. Carbery ◽  
J. Vance ◽  
S. Wainger ◽  
J. Wright
Keyword(s):  
Space Of Homogeneous Type ◽  
Homogeneous Type

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.

Real-Variable Characterizations of Hardy–Lorentz Spaces on Spaces of Homogeneous Type with Applications to Real Interpolation and Boundedness of Calderón–Zygmund Operators

2020 ◽  
Vol 8 (1) ◽  
pp. 182-260
Author(s):  
Xilin Zhou ◽  
Ziyi He ◽  
Dachun Yang
Keyword(s):  
Real Variable ◽  
Interpolation Theorem ◽  
Lorentz Spaces ◽  
Maximal Functions ◽  
Reference Points ◽  
Real Interpolation ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Geometrical Properties ◽  
Dyadic Cubes

AbstractLet (𝒳, d, μ) be a space of homogeneous type, in the sense of Coifman and Weiss, with the upper dimension ω. Assume that η ∈(0, 1) is the smoothness index of the wavelets on 𝒳 constructed by Auscher and Hytönen. In this article, via grand maximal functions, the authors introduce the Hardy–Lorentz spaces H_*^{p,q}\left( \mathcal{X} \right) with the optimal range p \in \left( {{\omega \over {\omega + \eta }},\infty } \right) and q ∈ (0, ∞]. When and p \in ({\omega \over {\omega + \eta }},1]q ∈ (0, ∞], the authors establish its real-variable characterizations, respectively, in terms of radial maximal functions, non-tangential maximal functions, atoms, molecules, and various Littlewood–Paley functions. The authors also obtain its finite atomic characterization. As applications, the authors establish a real interpolation theorem on Hardy–Lorentz spaces, and also obtain the boundedness of Calderón–Zygmund operators on them including the critical cases. The novelty of this article lies in getting rid of the reverse doubling assumption of μ by fully using the geometrical properties of 𝒳 expressed via its dyadic reference points and dyadic cubes and, moreover, the results in the case q ∈ (0, 1) of this article are also new even when 𝒳 satisfies the reverse doubling condition.

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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