The Converse of Fatou’s Theorem for Zygmund Measures

  • Joan J. Carmona, Juan J. Donaire
  • Published 1999
denote its Poisson integral defined on the upper halfplane Π+ = {(x, y) : y > 0}. Observe that P [μ](x, y) = Py ∗ μ(x), where Py(x) = 1 π y y2+x2 . Analogously, if f is a bounded function we can also write P [f ](x, y) = Py ∗ f(x). A classical Fatou theorem [10, p. 257] relates some differentiability properties of μ at x ∈ R to the asymptotic behaviour of u… CONTINUE READING