Square Functions Controlling Smoothness with Applications to Higher-Order Rectifiability

Series
Analysis Seminar
Time
Wednesday, April 17, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John Hoffman – Florida State University
Organizer
Benjamin Jaye

We present new results concerning characterizations of the spaces C1,α and “LIα+1” for 0<α<1.  The space LIα+1 is the space of Lipschitz functions with α-order fractional derivative having bounded mean oscillation.  These characterizations involve geometric square functions which measure how well the graph of a function is approximated by a hyperplane at every point and scale.  We will also discuss applications of these results to higher-order rectifiability.