Directional operators and radial functions on the plane |
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| Authors: | Javier Duoandikoetxea Ana Vargas |
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| Institution: | (1) Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain;(2) Departamento de Matemáticas, Universidad Autónoma de Madrid, E-28049 Madrid, Spain;(3) Present address: Department of Mathematics, Yale University, 06520 New Haven, CT, USA |
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| Abstract: | LetEçS 1 be a set with Minkowski dimensiond(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions ofE. The main result of this paper shows that these operators are bounded onL rad p (R2) forp>1+d(E) and unbounded whenp<1+d(E). We also give some end-point results. |
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