Geodesic
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain
Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 381-388

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DOI

It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces ${{A}^{P}}$ with $0 . The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products $B$ with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of ${B}'$ in the space ${{A}^{p}}\left( p>1 \right)$ . As a consequence, we prove that there exists a Blaschke product $B$ with zeros on a radius such that ${B}'\,\notin \,{{A}^{3/2}}$ .
DOI : 10.4153/CMB-2006-038-x
Mots-clés : 30D50, 30D55, 32A36, Blaschke products, Hardy spaces, Bergman spaces 
Girela, Daniel; Peláez, José Ángel. On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain. Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 381-388. doi: 10.4153/CMB-2006-038-x
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     author = {Girela, Daniel and Pel\'aez, Jos\'e \'Angel},
     title = {On the {Membership} in {Bergman} {Spaces} of the {Derivative} of a {Blaschke} {Product} {With} {Zeros} in a {Stolz} {Domain}},
     journal = {Canadian mathematical bulletin},
     pages = {381--388},
     year = {2006},
     volume = {49},
     number = {3},
     doi = {10.4153/CMB-2006-038-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-038-x/}
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