MAT 638. Topics in Real Analysis.

• TST for Lip graphs
• Extending maps into trees and applications ala Kaufman and Semmes. See ipage 12-16 in Hard-Sard: https://arxiv.org/abs/1105.4198
• Lip bilip for metric images (also state GC David version)
• Hoelder functions and martingale-style theorems
• David-Snipes proof of Naor-Neiman (Assuad improvement) https://arxiv.org/abs/1211.3223
• Mean oscillation, BMO,
• John-Nirenberg
• BMO from dyadic BMO
• Connection to UR. different definitions of UR
• Christ cubes
• show LI implies BPBI. and BI implies BPLG
• Show stability of beta_\infty sum under BP for k=1
• Fang-Jones example: example of beta_infty unbounded for graph of lip function R^3\to R. see example 1.16 in https://arxiv.org/pdf/1609.02892.pdf
• Dorronsoro's theorem: proof on page 51 of https://arxiv.org/pdf/1308.0558.pdf (Azzam) or use https://arxiv.org/pdf/1811.01702.pdf (Orponen)
• Coronization (use DS blue book)