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Article

Pradolini, Gladis ; Recchi, Jorgelina
Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces. (English). Czechoslovak Mathematical Journal, vol. 68 (2018), issue 1, pp. 77-94
MSC: 42B25 | MR 3783586 | Zbl 06861568 | DOI: 10.21136/CMJ.2018.0337-16
Keywords:
non-homogeneous space; generalized fractional operator; weight
Summary:
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 $0<n\leq d$. \endgraf 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).
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