6533b85afe1ef96bd12b9508
RESEARCH PRODUCT
Embedding of analytic function spaces with given mean growth of the derivative
Oscar BlascoM. Auxiliadora MárquezDaniel Girelasubject
Discrete mathematicssymbols.namesakeComplement (group theory)Function spaceGeneral MathematicssymbolsEmbeddingDerivativeHardy spaceSpace (mathematics)Unit (ring theory)MathematicsAnalytic functiondescription
MSC (2000) 30D55 If φ is a positive function defined in (0,1) and 0 <p< ∞, we consider the space L(p, φ) which consists of all functions f analytic in the unit disc D for which the integral means of the derivative Mp(r, f � )= " 1 2π Rπ −π þ f � (re iθ ) þ p dθ "1/p , 0 <r< 1, satisfy M p(r, f � )=O (φ(r)) ,a sr → 1. In this paper, for any given p ∈ (0,1), we characterize the functions φ, among a certain class of weight functions, to be able to embedd L(p, φ) into classical function spaces. These results complement other previously obtained by the authors for p ≥ 1. c
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-12-01 | Mathematische Nachrichten |