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BY 4.0 license Open Access Published by De Gruyter Open Access December 16, 2020

Radial growth of the derivatives of analytic functions in Besov spaces

Dedicated to the memory of Peter L. Duren

Salvador Domínguez and Daniel Girela EMAIL logo
From the journal Concrete Operators

Abstract

For 1 < p < ∞, the Besov space Bp consists of those functions f which are analytic in the unit disc 𝔻 = {z ∈ 𝔺 : |z| < 1} and satisfy ∫𝔻(1 − |z|2)p−2|f ′(z)|p dA(z) < ∞. The space B2 reduces to the classical Dirichlet space 𝒟. It is known that if f ∈ 𝒟then |f ′(re)| = 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 Bp (1 < p < ∞) an we give also an application of our them to questions concerning multipliers between Besov spaces.

MSC 2010: 30H25; 47B38

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Received: 2020-08-13
Accepted: 2020-10-07
Published Online: 2020-12-16

© 2020 Salvador Domínguez et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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