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Functional Inequalities in Sobolev Spaces: From Isocapacitary Estimates to Littlewood-Paley Theory

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

I begin the talk by giving a brief survey on various geometric and Sobolev-type inequalities and highlighting the role of entropy monotonicity and isocapacitary estimates in establishing such inequalities. I will then move on to presenting some ongoing work on the use of isocapacitary estimates and Littlewood-Paley g-functions in establishing functional-embedding type inequalities and finally describe some connections with the Beurling-Ahlfors operator, Burkholder functional and conjectures relating to quasiconvexity in the plane.

This talk is part of the Analysis seminar series.

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