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For 1 &lt;  p  &lt; ∞, the Besov space  B p   consists of those functions  f  which are analytic in the unit disc  = { z ∈   : | z | &lt; 1} and satisfy ∫(1 − | z | 2 )  p   −2 | f  ′( z )|  p  dA ( z ) &lt; ∞. The space  B  2  reduces to the classical Dirichlet space . It is known that if  f  ∈ then | f  ′( re iθ  )| = o[(1 −  r ) −1/2 ], for almost every ∈ [0, 2π]. 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 &lt;  p  &lt; ∞) an we give also an application of our them to questions concerning multipliers between Besov spaces.

Radial growth of the derivatives of analytic functions in Besov spaces: Dedicated to the memory of Peter L. Duren