Abstract
In this paper we study the spaces of continuous functionsf on ℝ2 satisfying $$\int_0^{2\pi } {f(z + \xi e^{r\theta } )} d\mu (\theta ) \to f(z)$$ (4) uniformly on compact sets as ξ → ∞, where μ is a finite complex Borel measure supported on the unit circle {z ∈ ℂ: ¦z¦=1} with ∫2π0 dμ(θ)=1. Our main result is the following:
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