Abstract
In this chapter necessary and sufficient conditions for boundedness of the fractional maximal functions \((\mathcal{M}_{\alpha(.)}f)(x) := \mathop{\rm{sup}}\limits_{{Q}\ni{x}} \frac{1}{\vert{Q}\vert^{1-\alpha(x)/{n}}} \int\limits_{Q} \vert{f}(y)\vert{dy}, \, \, \, 0 < \alpha_{-} \leqslant \alpha_{+} < {n}\), and Riesz potentials \((I^{\alpha(.)} {f})(x) := \int\limits_{\mathbb{R}^{n}} \frac{f(y)}{\vert{x - y}\vert^{n-\alpha(x)}}{dy}, \, \, \, 0 < \alpha_{-} \leqslant \alpha_{+} < {n}\) from L p(ℝn, w) to L q (.)(ℝn, v) are given in the case when the parameter α(.) and the weights are general-type functions.
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Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S. (2016). Two-weight Inequalities for Fractional Maximal Functions. In: Integral Operators in Non-Standard Function Spaces. Operator Theory: Advances and Applications, vol 248. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21015-5_6
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DOI: https://doi.org/10.1007/978-3-319-21015-5_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-21014-8
Online ISBN: 978-3-319-21015-5
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