University of Birmingham > Talks@bham > Analysis seminar > Subdyadic square functions and applications

Subdyadic square functions and applications

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If you have a question about this talk, please contact Alessio Martini.

We introduce variants of the classical Littlewood-Paley g-functions that decouple and recouple frequency decompositions at scales finer than dyadic. This allow us to obtain pointwise estimates for highly-singular Fourier multipliers on Rd satisfying regularity hypothesis at such finer scales.

As a consequence, we bound such multipliers by geometrically-defined maximal operators via L2-weighted inequalities. In particular, our results apply to oscillatory integral operators and solution operators for dispersive PDE , such as the time-dependent free Schrödinger equation. This is joint work with Jon Bennett.

This talk is part of the Analysis seminar series.

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