Counterexamples on non-α-normal functions with good integrability

Blaschke products are used to construct concrete examples of analytic functions with good integrability and bad behavior of spherical derivative. These examples are used to show that none of the classes M^#_p, 0 < p < ∞, is contained in the α-normal class N^α when 0 <α< 2.This implies that M^#_p is in a sense a much larger class than Q^#_p.