Bergman projections on Besov spaces on balls

Kaptanoglu, HT
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.


Besov spaces and Bergman projections on the ball
Kaptanoglu, HT (Elsevier BV, 2002-11-01)
A class of radial differential operators are investigated yielding a natural classification of diagonal Besov spaces on the unit ball of C-N. Precise conditions are given for the boundedness of Bergman projections from certain L-P spaces onto Besov spaces. Right inverses for these projections are also provided. Applications to complex interpolation are presented.
Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
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Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18)
In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
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Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2018-08-01)
Let E-G be a Gamma-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Gamma, where G and Gamma are complex linear algebraic groups. Suppose X is contractible as a topological Gamma-space with a dense orbit, and x(0) is an element of X is a Gamma-fixed point. We show that if Gamma is reductive, then E-G admits a Gamma-equivariant isomorphism with the product principal G-bundle X x rho E-G(x(0)), where rho : Gamma -> G is a homomorphism between algebraic...
Chirality of real non-singular cubic fourfolds and their pure deformation classification
Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22)
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.
Citation Formats
H. Kaptanoglu, “Bergman projections on Besov spaces on balls,” ILLINOIS JOURNAL OF MATHEMATICS, pp. 385–403, 2005, Accessed: 00, 2020. [Online]. Available: