Directional operators and mixed norms

  1. Duoandikoetxea Zuazo, Francisco Javier
Journal:
Publicacions matematiques

ISSN: 0214-1493

Year of publication: 2002

Volume: 46

Issue: 1

Pages: 39-56

Type: Article

DOI: 10.5565/PUBLMAT_ESCO02_03 DIALNET GOOGLE SCHOLAR lock_openDDD editor

More publications in: Publicacions matematiques

Abstract

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].