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Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type. (English) Zbl 1002.42009

Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón-Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type. By a space of nonhomogeneous type the authors mean a measure space with a quasimetric; however, the doubling condition is not assumed and may fail. In the nonhomogeneous case, the results of the authors are also new even in Lebesgue spaces.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
43A85 Harmonic analysis on homogeneous spaces
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.)
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