Resumen de p-Radial Exceptional Sets and Conformal Mappings

Piotr Kot

• For p > 0 and for a given set E of type Gdelta in the boundary of the unit disc partial {mathbb D} we construct a holomorphic function f \in {mathbb O} (mathbb D) such that \int{mathbb D} \setminus [0,1] E |f|p d mathfrak{L}2 < infty and E = Ep(f) = { z \in \partial {mathbb D} : \int01 |f(tz)|p dt = infty} .

  In particular if a set E has a measure equal to zero, then a function f is constructed as integrable with power p on the unit disc mathbb D.