Weighted Hardy-type operators on nonincreasing cones. (English) Zbl 1442.42041
Summary: In this paper, we obtain characterizations of the boundedness of multivariate weighted Hardy-type operators on monotone functions. We also study properties of the weight functions \(u\) on \(\mathbb{R}_+^n\) satisfying the condition \(B_p^{\vec{\phi}}\left( { \mathbb{R}_+^n} \right)\), which is an extension of the well-known conditions \(B_p\) and \({B_p}\left( { \mathbb{R}_+^n} \right)\). Finally, we give simpler characterizations of the boundedness of Hardy-type operators when the weight \(u\) admits separation of variables.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 47G10 | Integral operators |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
Keywords:
weighted Hardy-type operator; nonincreasing cone; characterization of weight; boundedness of operatorReferences:
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