Carlos Pérez- Fractional Poincaré Inequalities for Doubling and Non-Doubling Weights

Explore Fractional Poincaré inequalities for doubling and non-doubling weights in this 50-minute lecture. Delve into the unification and improvement of well-known results concerning Fractional Poincaré-Sobolev inequalities using flexible Harmonic Analysis methods. Learn about oscillation, self-improvement, and functional proofs while examining key points and sketches of general results. Investigate geometric conditions, motivations for new findings, and the main theorem involving non-doubling and reverse doubling weights. Gain insights from recent joint research as the speaker guides you through the proof and its implications in the field of mathematics.

Introduction
Motivation
Definition
Oscillation
Selfimprovement
Why
Functional Proof
Key Points
Sketch
General result
Geometric condition
Motivation for new result
Main result
Nondoubling weights
Reverse doubling weights
Proof