Comments on: “Sharp Weighted Estimates for Square Functions Associated to Operators on Spaces of Homogeneous Type ”

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Mahdi Hormozi ◽  
Kôzô Yabuta
Keyword(s):  
Homogeneous Type ◽  
Square Functions ◽  
Spaces Of Homogeneous Type ◽  
Weighted Estimates

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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