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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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