Directional operators and radial functions on the plane

Javier Duoandikoetxea Departamento de Matemáticas, Universidad del País Vasco Ana Vargas Departamento de Matemáticas, Universidad Autónoma de Madrid

TBD mathscidoc:1701.332837

Arkiv for Matematik, 33, (2), 281-291, 1994.6
Let$E$ç$S$^{1}be a set with Minkowski dimension$d(E)1$. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions of$E$. The main result of this paper shows that these operators are bounded on$L$_{$rad$}^{$p$}(R^{2}) for$p>1+d(E)$and unbounded when$p<1+d(E)$. We also give some end-point results.
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@inproceedings{javier1994directional,
  title={Directional operators and radial functions on the plane},
  author={Javier Duoandikoetxea, and Ana Vargas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203546143032646},
  booktitle={Arkiv for Matematik},
  volume={33},
  number={2},
  pages={281-291},
  year={1994},
}
Javier Duoandikoetxea, and Ana Vargas. Directional operators and radial functions on the plane. 1994. Vol. 33. In Arkiv for Matematik. pp.281-291. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203546143032646.
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