Weighted inequalities related to a Muckenhoupt and Wheeden problem for one-side singular integrals
In this paper we obtain for $T^+$, a one-sided singular integral given by a Calder´on-Zygmund kernel with support in $(-infty,0)$, a $L^p(w)$ bound when $win A_1^+$. A. K. Lerner, S. Ombrosi, and C. Pérez in ``$A_{1}$ Bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Whee...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2015 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/51845 |
| Online Access: | http://hdl.handle.net/11336/51845 |
| Access Level: | Open access |
| Keyword: | One-sided singular integrals Sawyer weights Weighted norm inequalities https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | In this paper we obtain for $T^+$, a one-sided singular integral given by a Calder´on-Zygmund kernel with support in $(-infty,0)$, a $L^p(w)$ bound when $win A_1^+$. A. K. Lerner, S. Ombrosi, and C. Pérez in ``$A_{1}$ Bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden, Math. Res. Lett. extbf{16} no. 1, (2009), 149-156" proved that this bound is sharp with respect to $||w||_{A_1} $ and with respect to $p$ . We also give a $L^{1,infty}(w)$ estimate, for a related problem of Muckenhoupt and Wheeden for $win A_1^+$ . We improve the classical results, for one-sided singular integrals, by putting in the inequalities a wider class of weights. |
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