### Square Functions Controlling Smoothness with Applications to Higher-Order Rectifiability

- Series
- Analysis Seminar
- Time
- Wednesday, April 17, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- John Hoffman – Florida State University

We present new results concerning characterizations of the spaces $C^{1,\alpha}$ and “$LI_{\alpha+1}$” for $0<\alpha<1$. The space $LI_{\alpha +1}$ is the space of Lipschitz functions with $\alpha$-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.