Growth and decrease of subharmonic functions in a cone
Consider subharmonic functions in the complex plane. If they satisfy the inequality \[ u(z)\leq a| z|^{\rho}+b;\quad a>0;\quad b\geq 0;\quad \rho >0 \] then Jensen's inequality simply offers integral estimations for u(z) and the corresponding Riesz-measure \(\mu\). The same problem is not trivial for subharmonic functions u(z) belonging to the half-plane and a variety of articles have contributed conditions to derive the desired integral estimations. The author shows that the methods due to literature are also helpful for subharmonic functions in a conus of \(R^ m\) thus generalizing the notion of order of subharmonic functions u(z) in a conus and integral estimations for u(z) and the corresponding Riesz- and surface measures.
scientific article; zbMATH DE number 4140142