Radial growth of the derivatives of analytic functions in Besov spaces

For 1 < p < infinity, the Besov space By consists of those functions f which are analytic in the unit disc IID = {z E C : vertical bar z vertical bar < 1} and satisfy integral(D)(1 - vertical bar z vertical bar(2))(P-2)vertical bar f'(z)(p) dA(z) < infinity. The space B-2 reduces to the classical Dirichlet space D. It is known that if f is an element of D then If (rei)1 = o[(1 - r)-112], for almost every theta is an element of [0, 2 pi]. Hallenbeck and Samotij proved that this result is sharp in a very strong sense. We obtain substitutes of the above results valid for the spaces B-p (1 < p < infinity) an we give also an application of our them to questions concerning multipliers between Besov spaces.