Some function spaces on spaces of homogeneous type

2001 ◽  
Vol 106 (2) ◽  
pp. 219-248 ◽  
Author(s):  
Manfred Kronz
Keyword(s):  
Function Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

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.

A unified method for maximal truncated Calderón–Zygmund operators in general function spaces by sparse domination

2019 ◽  
Vol 63 (1) ◽  
pp. 229-247
Author(s):  
Theresa C. Anderson ◽  
Bingyang Hu
Keyword(s):  
General Setting ◽  
Function Spaces ◽  
Weighted Norm ◽  
General Function ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Banach Function Spaces ◽  
Norm Inequalities ◽  
Unified Method

AbstractIn this note we give simple proofs of several results involving maximal truncated Calderón–Zygmund operators in the general setting of rearrangement-invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to track the dependence of the constants in weighted norm inequalities; additionally, our results hold in ℝn as well as in many spaces of homogeneous type.

scholarly journals Some Function Spaces Relative to Morrey-Campanato Spaces on Metric Spaces

2005 ◽  
Vol 177 ◽  
pp. 1-29 ◽  
Author(s):  
Dachun Yang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Metric Spaces ◽  
Function Spaces ◽  
Sharp Maximal Function ◽  
Embedding Theorems ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lizorkin Space

In this paper, the author introduces the Morrey-Campanato spaces Lsp(X) and the spaces Cps(X) on spaces of homogeneous type including metric spaces and some fractals, and establishes some embedding theorems between these spaces under some restrictions and the Besov spaces and the Triebel-Lizorkin spaces. In particular, the author proves that Lsp(X) = Bs∞,∞(X) if 0 < s < ∞ and µ(X) < ∞. The author also introduces some new function spaces Asp(X) and Bsp(X) and proves that these new spaces when 0 < s < 1 and 1 < p < ∞ are just the Triebel-Lizorkin space Fsp,∞(X) if X is a metric space, and the spaces A1p(X) and B1p(X) when 1 < p < ∞ are just the Hajłasz-Sobolev spaces W1p(X). Finally, as an application, the author gives a new characterization of the Hajłasz-Sobolev spaces by making use of the sharp maximal function.

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