A New Class of Inner Functions Uniformly Approximable by Interpolating Blaschke Products

2009 ◽  
Vol 5 (1) ◽  
pp. 219-235 ◽  
Author(s):  
Raymond Mortini
Keyword(s):  
Blaschke Products ◽  
Inner Functions ◽  
New Class ◽  
Interpolating Blaschke Products

Blaschke products in Lipschitz spaces

2009 ◽  
Vol 52 (3) ◽  
pp. 689-705 ◽  
Author(s):  
Miroljub Jevtić
Keyword(s):  
Blaschke Products ◽  
Lipschitz Spaces ◽  
Interpolating Blaschke Products

AbstractWe study the membership of Blaschke products in Lipschitz spaces, especially for interpolating Blaschke products and for those whose zeros lie in a Stolz angle. We prove several theorems that complement or extend the earlier works of Ahern and the author.

Cluster sets of interpolating Blaschke products

2005 ◽  
Vol 96 (1) ◽  
pp. 369-395 ◽  
Author(s):  
Pamela Gorkin ◽  
Raymond Mortini
Keyword(s):  
Blaschke Products ◽  
Cluster Sets ◽  
Interpolating Blaschke Products

scholarly journals Maximal subalgebra of Douglas algebra

1988 ◽  
Vol 11 (4) ◽  
pp. 735-741
Author(s):  
Carroll J. Gullory
Keyword(s):  
Blaschke Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Blaschke Products ◽  
Maximal Subalgebra ◽  
Interpolating Blaschke Product ◽  
Douglas Algebra ◽  
Necessary And Sufficient ◽  
Interpolating Blaschke Products ◽  
Douglas Algebras

Whenqis an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebraBofH∞[q¯]to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products inB. If the setM(B)⋂Z(q)is not open inZ(q), we also find a condition that guarantees the existence of a factorq0ofqinH∞such thatBis maximal inH∞[q¯]. We also give conditions that show when two arbitrary Douglas algebrasAandB, withA⫅Bhave property thatAis maximal inB.

scholarly journals Inner Functions in Lipschitz, Besov, and Sobolev Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Daniel Girela ◽  
Cristóbal González ◽  
Miroljub Jevtić
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Inner Function ◽  
Blaschke Products ◽  
Inner Functions ◽  
Finite Blaschke Products ◽  
The Subject

We study the membership of inner functions in Besov, Lipschitz, and Hardy-Sobolev spaces, finding conditions that enable an inner function to be in one of these spaces. Several results in this direction are given that complement or extend previous works on the subject from different authors. In particular, we prove that the only inner functions in either any of the Hardy-Sobolev spacesHαpwith1/p≤α<∞or any of the Besov spacesBαp,  qwith0<p,q≤∞andα≥1/p, except whenp=∞,α=0, and2<q≤∞or when0<p<∞,q=∞, andα=1/pare finite Blaschke products. Our assertion for the spacesB0∞,q,0<q≤2, follows from the fact that they are included in the spaceVMOA. We prove also that for2<q<∞,VMOAis not contained inB0∞,qand that this space contains infinite Blaschke products. Furthermore, we obtain distinct results for other values ofαrelating the membership of an inner functionIin the spaces under consideration with the distribution of the sequences of preimages{I-1(a)},|a|<1. In addition, we include a section devoted to Blaschke products with zeros in a Stolz angle.

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