F. G. Avkhadiev

Schwarz-pick type inequalities

1. Introduction.- 2. Basic coefficient inequalities.- 3. The Poincare metric.- 4. Basic Schwarz-Pick type inequalities.- 5. Punishing factors for special cases.- 6. Multiply connected domains.- 7. Related results.- 8. Some open problems.

Hardy-type inequalities on planar and spatial open sets

Several Hardy-type inequalities with explicit constants are proved for compactly supported smooth functions on open sets in the Euclidean space ℝn.

Sharp inequalities for the coefficients of concave schlicht functions

Let

A proof of the Livingston conjecture

D

Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space

denote the open unit disc and let

THE CONFORMAL RADIUS AS A FUNCTION AND ITS GRADIENT IMAGE

f\colon D\to \mathbb{C}

Schwarz-Pick Inequalities for Hyperbolic Domains in the Extended Plane

be holomorphic and injective in

Rellich type inequalities in domains of the Euclidean space

D

Hardy-type inequalities in arbitrary domains with finite inner radius

. We further assume that

Families of domains with best possible hardy constant

f(D)