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Weighted $$L_ \Phi$$ integral inequalities for maximal operators. (English) Zbl 0859.42017
Summary: Sufficient (almost necessary) conditions are given on the weight functions $$u(\cdot)$$, $$v(\cdot)$$ for $\Phi^{-1}_2\Biggl[\int_{\mathbb{R}^n}\Phi_2(C_2(M_sf)(x)) u(x)dx\Biggr]\leq \Phi^{-1}_1\Biggl[C_1 \int_{\mathbb{R}^n} \Phi_1(|f(x)|)v(x)dx\Biggr]$ to hold when $$\Phi_1$$, $$\Phi_2$$ are $$\varphi$$-functions with subadditive $$\Phi_1\Phi^{-1}_2$$ and $$M_s$$ $$(0\leq s<n)$$ is the usual fractional maximal operator.
##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
##### Keywords:
weighted inequalities; fractional maximal operator
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##### References:
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