The Brascamp–Lieb inequalities: recent developments
We discuss recent progress on issues surrounding the Brascamp–Lieb inequalities.
Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
We show that the maximal operator associated to the family of rectangles in one of whose sides is parallel to for some j,k is bounded on , . We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.
Variants of the Calderón-Zygmund theory for L-spaces.
The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea and Rubio...
The work of José Luis Rubio de Francia (IV).
José Luis and I first met at the famous - and hugely enjoyable 1983 El Escorial conference of which he and Ireneo Peral were the chief organisers, but we did not really discuss mathematics together until the spring and summer of 1985. There is an old question - formally posed by Stein in the proceedings of the 1978 Williamstown conference [St] - concerning the disc multiplier and the Bochner-Riesz means.
Pointwise Fourier Inversion and Localization in ...
Almost everywhere convergence of Fourier integrals in Rn
Hilbert transforms and maximal functions along rough flat curves.
Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L-localisation principle.
What is van der Corput's lemma in higher dimensions?
We consider variants of van der Corput's lemma in higher dimensions. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Restriction and decay for flat hypersurfaces.
In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ 1/(n+1) introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in R2. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature. In the...
Maximal functions and singular integrals associated to polynomial mapping of R.
Maximal functions and Hilbert transforms associated to polynomials.
Singular integrals and the Newton diagram.
We examine several scalar oscillatory singular integrals involving a real-analytic phase function φ(s,t) of two real variables and illustrate how one can use the Newton diagram of φ to efficiently analyse these objects. We use these results to bound certain singular integral operators.
Strichatz inequalities with weights in Morrey-Campanato classes.
A note on weighted estimates for the Schrödinger operator.
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