Harmonic analysis and the geometry of fractals
نویسنده
چکیده
Singular and oscillatory integral estimates such as maximal theorems and restriction estimates for measures on hypersurfaces have long been a central topic in harmonic analysis. We discuss the recent work by the author and her collaborators on the analogues of such results for singular measures supported on fractal sets. The common thread is the use of ideas from additive combinatorics. In particular, the additivecombinatorial notion of “pseudorandomness” for fractals turns out to be an appropriate substitute for the curvature of manifolds. Mathematics Subject Classification (2010). Primary 28A78, 42A38, 42B25, 26A24. Secondary 11B25, 42A45,
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تاریخ انتشار 2014