Directional operators and mixed norms

• Autores: Francisco Javier Duoandikoetxea Zuazo
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº Extra 1, 2002, págs. 39-56
• Idioma: inglés
• DOI: 10.5565/publmat_esco02_03
• Títulos paralelos:
  • Operadores direccionales y normas mixtas
• Enlaces
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• Resumen

  • We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered.

    [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].