Unconditional Haar bases for Lebesgue spaces on spaces of homogeneous type

2000 ◽  
Author(s):  
Hugo Aimar ◽  
Osvaldo Gorosito
Keyword(s):  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lebesgue Spaces

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.

scholarly journals Dyadic Fefferman–Stein inequalities and the equivalence of Haar bases on weighted Lebesgue spaces

2011 ◽  
Vol 141 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Hugo Aimar ◽  
Ana Bernardis ◽  
Luis Nowak
Keyword(s):  
Sufficient Conditions ◽  
General Setting ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Dyadic Systems ◽  
Vector Valued

We give sufficient conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these results, we prove a Fefferman–Stein weighted inequality for vector-valued dyadic Hardy–Littlewood maximal operators with dyadic weights in this general setting.

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.

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