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Weighted estimates for the Hilbert transform of odd functions. (English) Zbl 0805.42014

Author’s abstract: The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak, or extra-weak type estimates in Orlicz classes for the integral operator \[ H_ 0 f(x)= {2\over \pi} \int^ \infty_ 0 {yf(y)\over x^ 2- y^ 2} dy,\quad x\in (0,\infty). \] {}.
Reviewer: A.Seeger (Madison)

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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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References:

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