Directional operators and mixed norms
Copyright policy )Directional operators and mixed norms
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 Calder'on 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.
Directional Hilbert transform, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, directional Hilbert transform, mixed norms, directional Hardy-Littlewood maximal functions, Directional Hardy-Littlewood maximal functions, X-ray transform, Radon transform, Mixed norms, Potentials
Directional Hilbert transform, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, directional Hilbert transform, mixed norms, directional Hardy-Littlewood maximal functions, Directional Hardy-Littlewood maximal functions, X-ray transform, Radon transform, Mixed norms, Potentials
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