Punishing factors for special cases
Frontiers in mathematics · 2009
After a colloquium talk of the second author on estimates of the form for simply connected domains Ω and п in ℂ, Ch. Pommerenke ([132]) proposed to look at (5.1) in the following way. The quotient (λΩ(z))n/λп(f (z)) reflects the influence of the positions of the points z and f(z) in Ω and ∏ on the nth derivative f(n)(z), whereas the quantities Cn(Ω, п) are factors punishing bad behaviour of Ω or ү at the boundary. This motivates the title of the present chapter as well as the titles of some our papers.