Czechoslovak Mathematical Journal, first online, pp. 1-18


Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces

Gladis Pradolini, Jorgelina Recchi

Received June 27, 2016.   First published January 12, 2018.

Abstract:  Let $\mu$ be a nonnegative Borel measure on $\mathbb R^d$ satisfying that $\mu(Q)\le l(Q)^n$ for every cube $Q\subset\mathbb R^n$, where $l(Q)$ is the side length of the cube $Q$ and $0<n\leq d$. We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function $B$ in the context of non-homogeneous spaces related to the measure $\mu$. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W. Wang, C. Tan, Z. Lou (2012).
Keywords:  non-homogeneous space; generalized fractional operator; weight
Classification MSC:  42B25
DOI:  10.21136/CMJ.2018.0337-16

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Affiliations:   Gladis Pradolini, Facultad de Ingeniería Química (CONICET UNL), Santiago del Estero 2829, 3000 Santa Fe, Argentina, e-mail: gpradolini@santafe-conicet.gov.ar; Jorgelina Recchi, Instituto de Matemática Bahía Blanca (CONICET UNS), and Departamento de Matemáticas (UNS), Av. Alem 1253, 8000 Bahía Blanca, Argentina, e-mail: drecchi@uns.edu.ar


 
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