Czechoslovak Mathematical Journal, Vol. 68, No. 1, pp. 77-94, 2018
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).
Affiliations: Gladis Pradolini, Facultad de Ingeniería Química (CONICET UNL), Santiago del Estero 2829, 3000 Santa Fe, Argentina, e-mail: firstname.lastname@example.org; Jorgelina Recchi, Instituto de Matemática Bahía Blanca (CONICET UNS), and Departamento de Matemáticas (UNS), Av. Alem 1253, 8000 Bahía Blanca, Argentina, e-mail: email@example.com