Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of Cn.

• Autores: Patrick Ahern, Joaquim Bruna i Floris
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 4, Nº 1, 1988, págs. 123-153
• Idioma: inglés
• Títulos paralelos:
  • Caracterizaciones de integrales de área y funciones maximales en espacios de Hardy-Sobolev en la bola unidad de Cn.
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• Resumen

  • In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of Cn, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of Hp itself involving only complex-tangential derivatives.