Let Ω and Π be two simply connected domains in the complex plane C which are not equal to the whole plane C and let λΩ and λΠ denote the densities of the Poincaré metric in Ω and Π, respectively. For f : Ω → Π analytic in ...

Let Ω be an n-dimensional convex domain with finite inradius δ 0 = sup xεΩ δ, where δ = dist(x,ρΩ), and let (p,q) be a pair of positive numbers. For functions vanishing at the boundary of the domain and any v € [0, p/q] ...

As we have seen in Chapter 6 it is a very difficult task to find sharp punishing factors or substitutes for them in cases where multiply connected domains are involved. From this point of view, it seems natural that the ...

Let Ω be a domain in ℂ̄ with three or more boundary points in ℂ̄ and R(w, Ω) the conformal, resp. hyperbolic radius of Ω at the point w ∈ Ω \{∞}. We give a unified proof and some generalizations of a number of known theorems ...

Let Ω and ∏ be two simply connected proper subdomains of the complex plane ℂ. We are concerned with the set A(Ω, ∏) of functions f : Ω → ∏ holomorphic on Ω and we prove estimates for |f(n)(z)|, f ∈ A(Ω, Ω),z ∈ Ω, of the ...

Using the Bessel functions we obtain several weighted Hardy inequalities with sharp constants. The following inequality for absolutely continuous functions is a simple example: If p and ν are positive numbers, and f: [0, ...