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Two-weight, weak-type norm inequalities for singular integral operators

 

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Opened Access Two-weight, weak-type norm inequalities for singular integral operators
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Author: Cruz Uribe, David
Pérez Moreno, Carlos
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 1999
Published in: Mathematical Research Letters, 6 (4), 417-427.
Document type: Article
Abstract: 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.
Cite: Cruz Uribe, D. y Pérez Moreno, C. (1999). Generalized Poincare Inequalities: sharp self-improving properties. Mathematical Research Letters, 6 (4), 417-427.
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Format: PDF

URI: http://hdl.handle.net/11441/48500

DOI: 10.4310/MRL.1999.v6.n4.a4

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