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Multilinear restriction estimates on fractal sets

University of British Columbia

In harmonic analysis there is a rich history of restriction theory for measures supported on smooth manifolds, and recently much focus has turned to restriction for measures supported on fractal sets. On the other hand, the use of multilinear restriction estimates has propelled most current progress on classical restriction theory. In this thesis we discuss the existing literature on both of these main interests in restriction theory, and then consider their combination. We analyze the existence of multilinear restriction estimates for a collection of singular measures, particularly measures supported on Cantor sets. We generalize a linear restriction estimate of Chen to a multilinear setting and provide a class of Cantor sets to which this result applies. Furthermore, we give necessary conditions for the existence of multilinear restriction for singular measures. We are hopeful that the success of multilinear restriction estimates in furthering classical restriction theory may be reproduced in our context.

Text

2019-04-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69536

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/