Two-weight, weak-type norm inequalities for singular integral operators
We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log...
| Authors: | , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 1999 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/48500 |
| Online Access: | http://hdl.handle.net/11441/48500 https://doi.org/10.4310/MRL.1999.v6.n4.a4 |
| Access Level: | Open access |
| Keyword: | Weights Singular integral operators Calderón-Zygmund operators Maximal operators Orlicz spaces |
| Summary: | We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log L) p−1+δ,Q 1 |Q| Z Q v −p 0/p dx p/p0 ≤ K < ∞, δ > 0. This conditions is stronger than the Ap condition and is sharp since it fails when δ = 0. |
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