A Limit Case of the Hörmander Multiplier Theorem.
On quasiradial Fourier multiplier and their maximal functions.
Remarks on singular convolution operators
A note on Triebel-Lizorkin spaces
Inequalities for spherically symmetric solutions of the wave equation.
Fourier integral operators with fold singularities.
On oscillatory integral operators with folding canonical relations
Sharp estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation projects to T*X and T*Y with fold singularities.
Singular Radon transforms and maximal functions under convexity assumptions.
We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane.
Oscillatory and Fourier integral operators with degenerate canonical relations.
We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Problems on averages and lacunary maximal functions
We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an regularity result...
Two problems associated with convex finite type domains.
We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp L estimates for p > 4, generalizing the Carleson-Sjölin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.
A Calderón-Zygmund estimate with applications to generalized Radon transforms and Fourier integral operators
We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals.
Two endpoint bounds for generalized Radon transforms in the plane.
A variation norm Carleson theorem
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
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