WEIGHTED INEQUALITIES RELATED TO A MUCKENHOUPT AND WHEEDEN PROBLEM FOR ONE-SIDE SINGULAR INTEGRALS

MARÍA SILVINA RIVEROS; RAÚL EMILIO VIDAL

MATHEMATICAL INEQUALITIES & APPLICATIONS

ELEMENT

Lugar: Zagreb; Año: 2015 vol. 18 p. 1087 - 1109

1331-4343

In this paper we obtain for a one-sided singular integral given by a Calderón-Zygmund kernel with support in (−∞,0), a L^p(w) bound when w in Sawyer clases. In [A. K. Lerner, S. Ombrosi and C. Pérez, A_1 Bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden, Math. Res. Lett. 16 (2009), no. 1, 149-156.], the authors proved that this bound is sharp with respect to ||w||_{A_1} and with respect to p. We also give a L^{1,∞}(w) estimate, for a related problem of Muckenhoupt and Wheeden for w in Sawyer clases. We improve theclassical results, for one-sided singular integrals, by putting in the inequalities a wider class of weights.