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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. document.getElementById('cloakcc8189cc729299e19964d9d84154fae0').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addycc8189cc729299e19964d9d84154fae0 = 'c&#111;rv&#97;l&#97;' + '&#64;'; addycc8189cc729299e19964d9d84154fae0 = addycc8189cc729299e19964d9d84154fae0 + 'c&#97;mp&#117;s' + '&#46;' + '&#117;ngs' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r'; var addy_textcc8189cc729299e19964d9d84154fae0 = 'c&#111;rv&#97;l&#97;' + '&#64;' + 'c&#97;mp&#117;s' + '&#46;' + '&#117;ngs' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r';document.getElementById('cloakcc8189cc729299e19964d9d84154fae0').innerHTML += '<a ' + path + '\'' + prefix + ':' + addycc8189cc729299e19964d9d84154fae0 + '\'>'+addy_textcc8189cc729299e19964d9d84154fae0+'<\/a>';

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.