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A remark on singular integrals and power weights. (English) Zbl 0803.42004
Author’s abstract: “In this work we present several general theorems which imply the boundedness on weighted Lorentz spaces \(L^ p(| x|^ \alpha dx)\) for sublinear \(T\), which are known to be bounded in the unweighted case \(\alpha= 0\), under certain weak conditions on the size of \(T\). Applications are given to singular integrals and vector valued operators. In particular, we recover (and extend) some recent results by S. Hoffman on rough maximal and singular operators”.

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.)
42B25 Maximal functions, Littlewood-Paley theory
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