On Regularity Theorems for Linearly Invariant Families of Harmonic Functions (original) (raw)

Abstract

The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions f describes the growth character of different functionals of f ∈ S and z ∈ ∆ as z tends to ∂∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sensepreserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.

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