scholarly journals Orthonormal bases of regular wavelets in spaces of homogeneous type

2013 ◽  
Vol 34 (2) ◽  
pp. 266-296 ◽  
Author(s):  
Pascal Auscher ◽  
Tuomas Hytönen
Keyword(s):  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Orthonormal Bases

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.

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 trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

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