Rough maximal functions and rough singular integral operators applied to integrable radical functions

• Autores: Fernando Soria de Diego, Peter Sjögren
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 13, Nº 1, 1997, págs. 1-18
• Idioma: inglés
• Títulos paralelos:
  • Funciones de máximo y operadores integrales singulares, de primera aproximación, aplicados a funciones radiales integrables.
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• Resumen

  • Let O be homogeneous of degree 0 in Rn and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor O in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels O(y) / |y|n, provided that the mean value of O vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to arbitrary finite dimension, and to rough singular integrals.