A Plancherel–Polya Inequality in Besov Spaces on Spaces of Homogeneous Type

2018 ◽  
Vol 29 (2) ◽  
pp. 1571-1582
Author(s):  
Philippe Jaming ◽  
Felipe Negreira
Keyword(s):  
Besov Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications

2002 ◽  
Vol 9 (3) ◽  
pp. 567-590
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Entropy Numbers ◽  
Compact Embeddings

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

scholarly journals Besov spaces on spaces of homogeneous type and fractals

2003 ◽  
Vol 156 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

scholarly journals Smooth Decompositions of Triebel-Lizorkin and Besov Spaces on Product Spaces of Homogeneous Type

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Fanghui Liao ◽  
Zongguang Liu ◽  
Xiaojin Zhang
Keyword(s):  
Besov Spaces ◽  
Homogeneous Type ◽  
Product Spaces ◽  
Spaces Of Homogeneous Type ◽  
Calderón’S Reproducing Formula

We introduce Triebel-Lizorkin and Besov spaces by Calderón’s reproducing formula on product spaces of homogeneous type. We also obtain smooth atomic and molecular decompositions for these 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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