New subrepresentation forumlas connecting functions and their smoothness
The PDE & Analysis seminar covers topics in PDE and analysis.
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Description
Abstract: In this talk, we present recent work with Cong Hoang and Kabe Moen, where we extend the classical Sobolev-type subrepresentation formula
|f(x)| ≤ cn I1(|∇f|)(x),
where I1 is the classical fractional integral operator. First, we will show how to generalize I1 to a family of A1- potential type operators. Next, we show how the right-hand side can be further refined by using fractional derivatives instead of the |∇| operator, incorporating the Bourgain-Brezis-Mironescu factor. Lastly, we discuss the applications of these results to rough singular integral operators. We will highlight the connections to fundamental concepts such as isoperimetric inequalities and extrapolation theory.
Location
145 Hanna Neumann Building, room 1.33