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 Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

scholarly journals Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Chuang Chen ◽  
Ji Li ◽  
Fanghui Liao
Keyword(s):  
General Setting ◽  
Function Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Doubling Property ◽  
Full Generality ◽  
Orthonormal Bases ◽  
Additional Assumptions

Let(X,d,μ)be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metricdmay have no regularity and the measureμsatisfies only the doubling property. Adapting the recently developed randomized dyadic structures ofXand applying orthonormal bases ofL2(X)constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metricdand the measureμto the full generality of the theory of these function spaces.

Weighted modular estimates for a generalized maximal operator on spaces of homogeneous type

2010 ◽  
Vol 63 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Ana María Kanashiro ◽  
Gladis Pradolini ◽  
Oscar Salinas
Keyword(s):  
Maximal Operator ◽  
Homogeneous Type ◽  
Spaces Of 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.

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 Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type

2006 ◽  
Vol 80 (2) ◽  
pp. 229-262 ◽  
Author(s):  
Dongguo Deng ◽  
Dachun Yang
Keyword(s):  
Besov Space ◽  
Type Inequality ◽  
Space Of Homogeneous Type ◽  
Embedding Theorems ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lizorkin Space ◽  
Hardy Type ◽  
Riesz Operators ◽  
Type Spaces

AbstractLet (X, ρ, μ)d, θ be a space of homogeneous type with d < 0 and θ ∈ (0, 1], b be a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0 ∈ (0, 1) be some constant depending on d, ∈ and s. The authors introduce the Besov space bBspq (X) with a0 > p ≧ ∞, and the Triebel-Lizorkin space bFspq (X) with a0 > p > ∞ and a0 > q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov space b−1 Bs (X) and the Triebel-Lizorkin space b−1 Fspq (X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems, T b theorems, and the lifting property by introducing some new Riesz operators of these spaces.

Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams

2010 ◽  
Vol 53 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Justin Feuto ◽  
Ibrahim Fofana ◽  
Konin Koua
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Space Of Homogeneous Type ◽  
Weighted Norm ◽  
Fractional Operator ◽  
Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Orlicz Norm ◽  
Lebesgue Spaces ◽  
Norm Inequalities

AbstractWe give weighted norm inequalities for the maximal fractional operator ℳq,β of Hardy– Littlewood and the fractional integral Iγ. These inequalities are established between (Lq, Lp)α(X, d, μ) spaces (which are superspaces of Lebesgue spaces Lα(X, d, μ) and subspaces of amalgams (Lq, Lp)(X, d, μ)) and in the setting of space of homogeneous type (X, d, μ). The conditions on the weights are stated in terms of Orlicz norm.

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