Singularity and regularity -- local and global.
Modulation invariant and multilinear singular integral operators
In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...
A T(b) theorem with remarks on analytic capacity and the Cauchy integral
On local and global analytic and Gevrey hypoellipticity
Weighted norm inequalities and Schur's Lemma
Inversion in some algebras of singular integral operators.
A convolution inequality concerning Cantor-Lebesgue measures.
Weak type endpoint bounds for Bochner-Riesz multipliers.
Examples of singular maximal functions unbounded on L.
Singular and maximal Radon transforms: Analysis and geometry.
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