Quantitative Fatou Property (QFT) is a generalization of
Fatou Property deeply connected with the geometry of a domain. It turns
out that in R^{n} 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