Quantitative Fatou Property (QFT) is a generalization of Fatou Property deeply connected with the geometry of a domain. It turns out that in Rn QFT holds for harmonic functions if and only if boundary of a domain is uniformly rectifiable. I will show that QFT holds for upper half plane, which was proved by Garnett, and some generalization proved by Dahlberg for Lipschitz domains. It is worth noting that instead of taking harmonic functions one can take solutions of some elliptic equations and prove similar results which was done by Bortz and Hofmann.

Meeting ID: 824 6311 2693 Passcode: 940746