scholarly journals Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type

2006 ◽  
Vol 322 (2) ◽  
pp. 825-846 ◽  
Author(s):  
Ana Bernardis ◽  
Silvia Hartzstein ◽  
Gladis Pradolini
Keyword(s):  
Fractional Integrals ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Spaces Of Homogeneous Type

Two-weighted inequalities for maximal operators related to Schrödinger differential operator

2020 ◽  
Vol 32 (6) ◽  
pp. 1415-1439
Author(s):  
Maria Amelia Vignatti ◽  
Oscar Salinas ◽  
Silvia Hartzstein
Keyword(s):  
Fractional Integral ◽  
Schrödinger Operators ◽  
Finite Measure ◽  
The Other ◽  
Maximal Operators ◽  
Schrodinger Operators ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Spaces Of Homogeneous Type ◽  
Measure Spaces

AbstractWe introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.

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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