Harmonic analysis
Description
Many problems in harmonic analysis involve substantial geometric considerations at their core; perhaps one of the most infamous example is the Kakeya conjecture. One family of problems in which I am particularly interested are ‘fractal’ versions of classical questions, such as the Lp-improving properties of maximal operators with restricted dilation sets, or generalizations such as local smoothing estimates for the wave equation with time restricted to a fractal subset.
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Relevant Research Articles
- A fractal local smoothing problem for the wave equation
With: David Beltran, Joris Roos, Andreas Seeger Journal: Preprint (submitted) Links: pdfarxiv