Artículo
Exponential decay estimates for singular integral operators
Autor/es | Ortiz Caraballo, Carmen María
Pérez Moreno, Carlos Rela, Ezequiel |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2013-12 |
Fecha de depósito | 2016-06-15 |
Publicado en |
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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 ... 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 functions and vector valued extensions of both maximal functions and Calderón–Zygmund operators. In each case, M will be replaced by a suitable maximal operator. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España Junta de Andalucía |
Identificador del proyecto | MTM2009-08934
FQM-4745 |
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. |
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