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Exponential decay estimates for singular integral operators

Opened Access Exponential decay estimates for singular integral operators

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Autor: Ortiz Caraballo, Carmen María
Pérez Moreno, Carlos
Rela, Ezequiel
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2013-12
Publicado en: Mathematische Annalen, 357 (4), 1217-1243.
Tipo de documento: Artículo
Resumen: The following subexponential estimate for commutators is proved |{x ∈ Q : |[b, T]f(x)| > tM2 f(x)}| ≤ c e− √ α tkbkBMO |Q|, t > 0. where c and α are absolute constants, T is a Calder´on–Zygmund operator, M is the Hardy Littlewood maximal function and f is any function supported on the cube Q ⊂ Rn. We also obtain that |{x ∈ Q : |f(x) − mf (Q)| > tM# λn;Q(f)(x)}| ≤ c e−α t|Q|, t > 0, where mf (Q) is the median value of f on the cube Q and M# λn;Q is Str¨omberg’s local sharp maximal function with λn = 2−n−2 . As a consequence we derive Karagulyan’s estimate: |{x ∈ Q : |T f(x)| > tM f(x)}| ≤ c e−c t |Q| t > 0, from improving Buckley’s theorem. A completely different approach is used based on a combination of “Lerner’s formula” with some special weighted estimates of Coifman-Fefferman type obtained via Rubio de Francia’s algorithm. The method is flexible enough to derive similar estimates for other operators such as multilinear Calderón–Zygmund operators, dyadic and continuous square fun...
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Cita: Ortiz Caraballo, C.M., Pérez Moreno, C. y Rela, E. (2013). Exponential decay estimates for singular integral operators. Mathematische Annalen, 357 (4), 1217-1243.
Tamaño: 299.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42362

DOI: 10.1007/s00208-013-0940-3

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