scholarly journals A commutator theorem for fractional integrals in spaces of homogeneous type

2000 ◽  
Vol 24 (6) ◽  
pp. 403-418 ◽  
Author(s):  
Jorge J. Betancor
Keyword(s):  
Fractional Integrals ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Commutator Theorem

We give a new proof of a commutator theorem for fractional integrals in spaces of homogeneous type.

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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