Integral means of harmonic univalent functions

Abstract EN

Let SH denote the class of all functions f = h + g that are complex-valued, harmonic, orientation preserving, and univalent in the open unit disc U, where h and g are analytic in U.

In this paper we show that if fЄ SH and h has a bounded spherical area, then the radial limits for h, g, and f exist everywhere except for a set of logarithmic capacity zero.

We also show that if f e SH and/is convex or close-to-convex, then h, g Є Hp and/Є hp, for some specific values of p > 0, where Hp and h p are the Hardy spaces of order p for analytic and harmonic functions respectively.