A new of looking at distributional estimates; applications for the bilinear Hilbert transform.

Título inglés	A new of looking at distributional estimates; applications for the bilinear Hilbert transform.
Título español	Una nueva forma de considerar las estimaciones distribucionales; aplicaciones para la transformada bilineal de Hilbert.
Autor/es	Bilyk, Dimitriy ; Grafakos, Loukas
Organización	Sch. Math. Georgia Inst. Technol., Atlanta (Georgia), Estados Unidos;Dep. Math. Univ. Missouri, Columbia (Missouri), Estados Unidos
Revista	0010-0757
Publicación	2006, 57 (Extra): 141-169, 18 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable over compact sets. They also provide restricted type endpoint results on products of Lebesgue spaces where one exponent is 1 or the sum of the reciprocal of the exponents is 3/2. The proof of the distributional estimates for the bilinear Hilbert transform rely on an improved energy estimate for characteristic functions with respect to sets of tiles from which appropriate exceptional subsets have been removed.
Clasificación UNESCO	120213
Palabras clave español	Análisis de Fourier ; Operadores multilineales ; Transformada de Hilbert
Código MathReviews	MR2264208
Código Z-Math	Zbl 1112.42006
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