Illinois Journal of Mathematics

Bergman projections on Besov spaces on balls

H. Turgay Kaptanoğlu

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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

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

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

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)


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

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