Damping oscillatory integrals with polynomial phase.
Dimension free estimates for the bilinear Riesz transform.
Dirac operators, conformal transformations and aspects of classical harmonic analysis.
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 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...
Discrete analogues of singular and maximal Radon transforms.
Distinctness of spaces of Lorentz-Zygmund multipliers
We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.
Distributional fractional powers of the Laplacean. Riesz potentials
For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...
Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields
Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.