Illinois Journal of Mathematics

Bergman projections on Besov spaces on balls

H. Turgay Kaptanoğlu

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Abstract

Extended Bergman projections from Lebesgue classes onto all Besov spaces on the unit ball are defined and characterized. Right inverses and adjoints of the projections share the property that they are imbeddings of Besov spaces into Lebesgue classes via certain combinations of radial derivatives. Applications to the Gleason problem at arbitrary points in the ball, duality, and complex interpolation in Besov spaces are obtained. The results apply, in particular, to the Hardy space $H^2$, the Arveson space, the Dirichlet space, and the Bloch space.

Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 385-403.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138024

Digital Object Identifier
doi:10.1215/ijm/1258138024

Mathematical Reviews number (MathSciNet)
MR2163941

Zentralblatt MATH identifier
1079.32004

Subjects
Primary: 32A36: Bergman spaces
Secondary: 32A18: Bloch functions, normal functions 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 46E15: Banach spaces of continuous, differentiable or analytic functions 46E20: Hilbert spaces of continuous, differentiable or analytic functions 47B38: Operators on function spaces (general)

Citation

Kaptanoğlu, H. Turgay. Bergman projections on Besov spaces on balls. Illinois J. Math. 49 (2005), no. 2, 385--403. doi:10.1215/ijm/1258138024. https://projecteuclid.org/euclid.ijm/1258138024


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