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Session S38 - Geometric Potential Analysis

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Sufficient conditions for some two-weighted inequalities for singular integrals

Álvaro Corvalán

Universidad Nacional de General Sarmiento, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

They are quite well known several relationships between $A_p$ Muckenhoupt's weight functions and weighted inequalities for many singular integrals, like Riesz potentials, Riesz transforms, and the Hilbert trans-form. For instance it is a quite straightforward result of E. Stein that the weights for which all the Riesz Transformations are of weak type $(p,p)$ must be $A_p$ weights, or from the Helson-Szeg\"o you can deduce that the weights $w$ for which the Hilbert transform is bounded in $L^2(w)$ are $A2$-weights. In this presentation we give some conditions for pairs of weights involving two-weighted inequalities.

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