Resumen de Directional operators and mixed norms

Francisco Javier Duoandikoetxea Zuazo

• 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].