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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1434 - 1462
We extend the classical theory of Qp-spaces of Aulaskari, Xiao and Zhao in two directions: first, by considering more general construction of such spaces; and... 
Möbius invariance | [formula omitted]-spaces | Bloch space
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1434 - 1462
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, p. 1434
We extend the classical theory of Q.sub.p-spaces of Aulaskari, Xiao and Zhao in two directions: first, by considering more general construction of such spaces;... 
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 1, pp. 233 - 272
We give a complete description of the boundary behaviour of the Poisson kernel and the harmonic Bergman kernel of a bounded domain with smooth boundary, which... 
Poisson kernel | Harmonic Bergman kernel | Pseudodifferential boundary operators | MATHEMATICS | MATHEMATICS, APPLIED | SPACES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 780 - 826
We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by... 
Symmetric domain | Reproducing kernel | Asymptotic expansion | Normal algebraic variety | MATHEMATICS | BALL | TOEPLITZ-OPERATORS | HANKEL-OPERATORS
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 03/2019, Volume 64, Issue 3, pp. 519 - 540
We show that the usual Poincaré metric is the only radial balanced metric on the disc with not too wild boundary behaviour. Additionally, we identify... 
32Q15 | 32A36 | 53C55 | Balanced metric | strictly pseudoconvex domain | Bergman kernel | 30F45 | MATHEMATICS | SCALAR CURVATURE
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2016, Volume 271, Issue 5, pp. 1243 - 1261
For weights ρ which are either radial on the unit ball or depend only on the vertical coordinate on the upper half-space, we describe the asymptotic behaviour... 
Asymptotic expansion | Bergman kernel | Harmonic Bergman kernel | MATHEMATICS | BALL | BEREZIN TRANSFORM | UNIT | REPRODUCING KERNELS | SPACES | THEOREM | QUANTIZATION
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2015, Volume 278, p. 254
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 367, Issue 1, pp. 75 - 97
We show that the Berezin transform associated to the harmonic Fock (Segal–Bargmann) space on C n has an asymptotic expansion analogously as in the holomorphic... 
Berezin transform | Harmonic Bergman kernel | Asymptotic expansion | Horn hypergeometric functions | Harmonic Fock space | MATHEMATICS | MATHEMATICS, APPLIED | UNIT | TOEPLITZ QUANTIZATION | OPERATORS | BERGMAN SPACES | KERNELS | Universities and colleges
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 12/2015, Volume 60, Issue 12, pp. 1712 - 1726
We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the... 
Bergman space | Primary: 32M15 | Secondary: 32A36 | 46E35 | bounded symmetric domain | Sobolev space | MATHEMATICS | RECURRENCE FORMULAS | OPERATORS | Eulers equations | Mathematical analysis | Decomposition | Complex variables | Formulas (mathematics) | Standards | Symmetry
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 6, pp. 1419 - 1457
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a... 
Toeplitz operator | Pseudodifferential operator | Sobolev space | Bergman kernel | MATHEMATICS | pseudodifferential operator | PSEUDOCONVEX DOMAINS | BIHOLOMORPHIC-MAPPINGS | HOLOMORPHIC-FUNCTIONS | COMPLEX POWERS | PROJECTIONS | ELLIPTIC PSEUDODIFFERENTIAL-OPERATORS | BOUNDARY-BEHAVIOR
Journal Article
Operator Theory: Advances and Applications, ISSN 0255-0156, 2016, Volume 251, pp. 69 - 115
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2015, Volume 278, pp. 254 - 254
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 8/2018, Volume 34, Issue 8, pp. 1297 - 1312
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2015, Volume 274, pp. 606 - 630
We prove the Arveson–Douglas essential normality conjecture for graded Hilbert submodules that consist of functions vanishing on a given homogeneous subvariety... 
Generalized Toeplitz operator | Arveson–Douglas conjecture | Secondary | Primary | Arveson-Douglas conjecture | MATHEMATICS | PSEUDOCONVEX DOMAINS | WEIGHTED BERGMAN KERNELS | TOEPLITZ-OPERATORS | SUBMODULES | ESSENTIAL NORMALITY
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 07/2016, Volume 271, Issue 2, pp. 264 - 288
For a class of O(n+1,R) invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the... 
Tian–Yau–Zelditch expansion | Bergman kernel | Kepler manifold | Balanced metric | Tian-Yau-Zelditch expansion | KAHLER-MANIFOLDS | SPACES | THEOREM | VARIETIES | SCALAR CURVATURE | MATHEMATICS | PROJECTION | MINIMAL BALL | QUANTIZATION | Mathematics
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2009, Volume 361, Issue 2, pp. 1039 - 1052
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2012, Volume 389, Issue 2, pp. 1086 - 1104
We give criteria for boundedness of the associated Bergman-type projections on Lp spaces on Cn with respect to generalized Gaussian weights exp(−|z|2m), m>0.... 
Reproducing kernel | Higher order Fock space | Bergman projection | Mittag–Leffler function | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL ASYMPTOTICS | OPERATORS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2009, Volume 361, Issue 3, pp. 1173 - 1188
We show that, perhaps surprisingly, in several aspects the behaviour of the reproducing kernels of Toeplitz operators and of the Berezin transform on some... 
Unit ball | Mathematical theorems | Differential operators | Analytic functions | Steepest descent method | Mathematical functions | Mathematics | Polynomials | Complex variables | Rotation | Berezin transform | Pluriharmonic Bergman kernel | pluriharmonic Bergman kernel | MATHEMATICS | TOEPLITZ QUANTIZATION | DOMAINS | KERNELS
Journal Article
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