Integral Equations and Operator Theory, ISSN 0378-620X, 8/2019, Volume 91, Issue 4, pp. 1 - 30

We completely characterize in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by Bergman–Besov kernels...

Inclusion relation | 32A37 | Integral operator | 45P05 | Bergman–Besov kernel | 32A36 | Secondary 32A55 | Schur test | Mathematics | 30H25 | 30H20 | Bergman–Besov space | Bloch–Lipschitz space | 46E15 | Bergman–Besov projection | 47G10 | Analysis | Radial fractional derivative | Forelli–Rudin estimate | Primary 47B34 | MATHEMATICS | Forelli-Rudin estimate | Bergman-Besov space | Bloch-Lipschitz space | Bergman-Besov kernel | SPACES | PROJECTIONS | Bergman-Besov projection

Inclusion relation | 32A37 | Integral operator | 45P05 | Bergman–Besov kernel | 32A36 | Secondary 32A55 | Schur test | Mathematics | 30H25 | 30H20 | Bergman–Besov space | Bloch–Lipschitz space | 46E15 | Bergman–Besov projection | 47G10 | Analysis | Radial fractional derivative | Forelli–Rudin estimate | Primary 47B34 | MATHEMATICS | Forelli-Rudin estimate | Bergman-Besov space | Bloch-Lipschitz space | Bergman-Besov kernel | SPACES | PROJECTIONS | Bergman-Besov projection

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 10/2018, Volume 291, Issue 14-15, pp. 2236 - 2251

We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new...

Sobolev imbedding | 32A05 | Primary: 30H05 | 32A36 | Besov | Hadamard gap series | Ryll–Wojtaszczyk polynomial | Lipschitz space | bounded holomorphic function | Bergman | 30H25 | 30H20 | 32A18 | Littlewood–Paley inequality | inclusion | 46E15 | atomic decomposition | 42B25 | 32W05 | Bloch | 32A37; Secondary: 30B10

Sobolev imbedding | 32A05 | Primary: 30H05 | 32A36 | Besov | Hadamard gap series | Ryll–Wojtaszczyk polynomial | Lipschitz space | bounded holomorphic function | Bergman | 30H25 | 30H20 | 32A18 | Littlewood–Paley inequality | inclusion | 46E15 | atomic decomposition | 42B25 | 32W05 | Bloch | 32A37; Secondary: 30B10

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2014, Volume 16, Issue 5, pp. 1350034 - 1-1350034-49

We obtain all Dirichlet spaces ℱq, q ∈ ℝ, of holomorphic functions on the unit ball of ℂN as weighted symmetric Fock spaces over ℂN. We develop the basics of...

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | MATHEMATICS, APPLIED | BESOV-SPACES | DIRICHLET SPACES | INTERPOLATION | MATHEMATICS | ALGEBRAS | BERGMAN SPACES | BALL | TOEPLITZ-OPERATORS | STANDARD MODELS | HILBERT-SPACE | C-algebra | Functions (mathematics) | Operators | Algebra | Mathematical analysis | Inequalities | Multivariable | Dirichlet problem | Touch

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | MATHEMATICS, APPLIED | BESOV-SPACES | DIRICHLET SPACES | INTERPOLATION | MATHEMATICS | ALGEBRAS | BERGMAN SPACES | BALL | TOEPLITZ-OPERATORS | STANDARD MODELS | HILBERT-SPACE | C-algebra | Functions (mathematics) | Operators | Algebra | Mathematical analysis | Inequalities | Multivariable | Dirichlet problem | Touch

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 08/2016, Volume 27, Issue 9, p. 1650070

We initiate a detailed study of two-parameter Besov spaces on the unit ball of ℝ n consisting of harmonic functions whose sufficiently high-order radial...

Bergman space | boundary growth | Gegenbauer (ultraspherical) polynomial | Gleason problem | Möbius transformation | Fourier coefficient | reproducing kernel | duality | Besov space | Poisson kernel | atomic decomposition | interpolation | zonal harmonic | radial fractional derivative | Spherical harmonic | Bergman projection | Hardy space | MATHEMATICS | R-N | Mobius transformation | BERGMAN SPACES | REPRODUCING KERNELS | TOEPLITZ-OPERATORS | UNIT BALL | BLOCH | PROJECTIONS

Bergman space | boundary growth | Gegenbauer (ultraspherical) polynomial | Gleason problem | Möbius transformation | Fourier coefficient | reproducing kernel | duality | Besov space | Poisson kernel | atomic decomposition | interpolation | zonal harmonic | radial fractional derivative | Spherical harmonic | Bergman projection | Hardy space | MATHEMATICS | R-N | Mobius transformation | BERGMAN SPACES | REPRODUCING KERNELS | TOEPLITZ-OPERATORS | UNIT BALL | BLOCH | PROJECTIONS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2007, Volume 250, Issue 2, pp. 483 - 520

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of C N are characterized in terms of Berezin transforms and Bergman-metric balls....

growth space | Cesàro-type operator | Carleson measure | Lacunary series | Besov | Bergman | Hardy | Lipschitz | Forelli–Rudin-type operator | Bergman metric | Weak | Hardy–Littlewood inequality | Fejér–Riesz | Separated sequence | Berezin transform | ultraweak convergence | Arveson | Dirichlet | Bergman projection | Schatten–von Neumann ideal | Bloch | Fejér-Riesz | Schatten-von Neumann ideal | Forelli-Rudin-type operator | Hardy-Littlewood inequality | weak, ultraweak convergence | INEQUALITIES | DIRICHLET TYPE | Cesaro-type operator | WEIGHTED BERGMAN SPACES | MATHEMATICS | separated sequence | Fejer-Riesz | Besov, Bergman, Dirichlet, Hardy, Arveson, Bloch, Lipschitz growth space | PROJECTIONS | OPERATORS | DOMAINS

growth space | Cesàro-type operator | Carleson measure | Lacunary series | Besov | Bergman | Hardy | Lipschitz | Forelli–Rudin-type operator | Bergman metric | Weak | Hardy–Littlewood inequality | Fejér–Riesz | Separated sequence | Berezin transform | ultraweak convergence | Arveson | Dirichlet | Bergman projection | Schatten–von Neumann ideal | Bloch | Fejér-Riesz | Schatten-von Neumann ideal | Forelli-Rudin-type operator | Hardy-Littlewood inequality | weak, ultraweak convergence | INEQUALITIES | DIRICHLET TYPE | Cesaro-type operator | WEIGHTED BERGMAN SPACES | MATHEMATICS | separated sequence | Fejer-Riesz | Besov, Bergman, Dirichlet, Hardy, Arveson, Bloch, Lipschitz growth space | PROJECTIONS | OPERATORS | DOMAINS

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2011, Volume 15, Issue 1, pp. 101 - 127

Isometry | Hermitian metric | Kahler metric | Growth | Duality | Gleason problem | Lipschitz | Besov space | Laplace-Beltrami operator | Zygmund | Mobius invariance | Decent functional | Interpolation | Slice function | Boundary growth | Geodesic completeness | Holomorphic sectional curvature | Bers | Taylor coefficient | Bergman projection | Bloch | Extremal point evaluation | Maximal space

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2012, Volume 57, Issue 6, pp. 667 - 675

We show that Drury's proof of the generalisation of the von Neumann inequality to the case of contractive rows of N-tuples of commuting operators still holds...

Secondary 46A32 | Primary 47A60 | von Neumann inequality | tensor products | 47B32 | 47S10 | quaternionic Hilbert spaces | reproducing kernel Hilbert spaces | Drury-Arveson space | MATHEMATICS | BALL | PRODUCT | Estimates | Cybernetics | Quantum theory | Inequality | Operators | Tensors | Mathematical analysis | Inequalities | Proving | Hilbert space | Complex variables

Secondary 46A32 | Primary 47A60 | von Neumann inequality | tensor products | 47B32 | 47S10 | quaternionic Hilbert spaces | reproducing kernel Hilbert spaces | Drury-Arveson space | MATHEMATICS | BALL | PRODUCT | Estimates | Cybernetics | Quantum theory | Inequality | Operators | Tensors | Mathematical analysis | Inequalities | Proving | Hilbert space | Complex variables

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 05/2007, Volume 58, Issue 1, pp. 1 - 33

We define Toeplitz operators on all Dirichlet spaces on the unit ball of $$\mathbb{C}^{N}$$ and develop their basic properties. We characterize bounded,...

Carleson measure | Besov | Primary 47B35, 32A37 | Bergman | Mathematics | Toeplitz operator | Hardy | Secondary 47B07, 47B10, 47B37, 47B33, 46E22, 32A36, 32A35 | Bergman metric | Arveson space | m -isometry | weighted shift | Schatten-von Neumann ideal | Analysis | Berezin transform | unitary equivalence | Dirichlet | Bergman projection | weak convergence | Weighted shift | Unitary equivalence | Weak convergence | M-isometry | THEOREM | BESOV-SPACES | HANKEL | BERGMAN SPACE | COMPACT-OPERATORS | INTERPOLATION | MATHEMATICS | BALL | m-isometry | INVARIANT SUBSPACES | PROJECTIONS

Carleson measure | Besov | Primary 47B35, 32A37 | Bergman | Mathematics | Toeplitz operator | Hardy | Secondary 47B07, 47B10, 47B37, 47B33, 46E22, 32A36, 32A35 | Bergman metric | Arveson space | m -isometry | weighted shift | Schatten-von Neumann ideal | Analysis | Berezin transform | unitary equivalence | Dirichlet | Bergman projection | weak convergence | Weighted shift | Unitary equivalence | Weak convergence | M-isometry | THEOREM | BESOV-SPACES | HANKEL | BERGMAN SPACE | COMPACT-OPERATORS | INTERPOLATION | MATHEMATICS | BALL | m-isometry | INVARIANT SUBSPACES | PROJECTIONS

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 1/2011, Volume 10, Issue 2, pp. 483 - 500

We investigate some relations between the reproducing kernels of Hilbert spaces of holomorphic and harmonic functions on the unit balls and the radial...

Bergman space | 32A37 | Computational Mathematics and Numerical Analysis | 32A36 | Functions of a Complex Variable | radial differential operator | 33C55 | Besov | 26A33 | Mathematics | Hardy | 31B05 | 31C25 | Drury-Arveson | 46E15 | spherical harmonic | 46E22 | Analysis | 47B34 | 46E20 | Dirichlet | reproducing kernel Hilbert space

Bergman space | 32A37 | Computational Mathematics and Numerical Analysis | 32A36 | Functions of a Complex Variable | radial differential operator | 33C55 | Besov | 26A33 | Mathematics | Hardy | 31B05 | 31C25 | Drury-Arveson | 46E15 | spherical harmonic | 46E22 | Analysis | 47B34 | 46E20 | Dirichlet | reproducing kernel Hilbert space

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 2009, Volume 347, Issue 13, pp. 735 - 738

Besov spaces of harmonic functions on the unit ball of R n are defined by requiring sufficiently high-order derivatives of functions lie in harmonic Bergman...

INTERPOLATION | MATHEMATICS | HOLOMORPHIC-FUNCTIONS | BERGMAN SPACES | UNIT BALL | BLOCH | SOBOLEV | Computer science

INTERPOLATION | MATHEMATICS | HOLOMORPHIC-FUNCTIONS | BERGMAN SPACES | UNIT BALL | BLOCH | SOBOLEV | Computer science

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 3/2002, Volume 42, Issue 1, pp. 1 - 21

We solve Gleason's problem in the reproducing kernel Hilbert space with repoducing kernel $$1/\left( {1 - \sum\nolimits_1^N {z_j w_j^* } } \right)$$ . We...

Secondary: 32A70 | Mathematics | Primary: 47A57 | Analysis | MATHEMATICS | SPACES

Secondary: 32A70 | Mathematics | Primary: 47A57 | Analysis | MATHEMATICS | SPACES

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 2006, Volume 343, Issue 7, pp. 453 - 456

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of C N are defined using imbeddings into Lebesgue classes via radial derivatives....

MATHEMATICS | BERGMAN PROJECTIONS

MATHEMATICS | BERGMAN PROJECTIONS

Journal Article

Illinois Journal of Mathematics, ISSN 0019-2082, 06/2005, Volume 49, Issue 2, pp. 385 - 403

Extended Bergman projections from Lebesgue classes onto all Besov spaces on the unit ball are defined and characterized. Right inverses and adjoints of the...

BOUNDED SYMMETRICAL DOMAINS | INTERPOLATION | MATHEMATICS | BLOCH SPACE | HANKEL-OPERATORS | HARDY | GLEASONS PROBLEM | KERNELS

BOUNDED SYMMETRICAL DOMAINS | INTERPOLATION | MATHEMATICS | BLOCH SPACE | HANKEL-OPERATORS | HARDY | GLEASONS PROBLEM | KERNELS

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 2006, Volume 17, Issue 3, pp. 407 - 423

We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace-Beltrami operators associated with the hyperbolic metric of the unit ball in ℂ...

Harnack inequality | Real hyperbolic space | Spherical harmonics | Weighted Laplace-Beltrami operator | Generalized Poisson kernel | Maximum principle | Invariant harmonic | Bohr radius | BALL | generalized Poisson kernel | BASES | INEQUALITY | maximum principle | real hyperbolic space | MATHEMATICS | spherical harmonics | ALGEBRAS | RADIUS | VARIABLES | POWER-SERIES THEOREM | weighted Laplace-Beltrami operator | invariant harmonic

Harnack inequality | Real hyperbolic space | Spherical harmonics | Weighted Laplace-Beltrami operator | Generalized Poisson kernel | Maximum principle | Invariant harmonic | Bohr radius | BALL | generalized Poisson kernel | BASES | INEQUALITY | maximum principle | real hyperbolic space | MATHEMATICS | spherical harmonics | ALGEBRAS | RADIUS | VARIABLES | POWER-SERIES THEOREM | weighted Laplace-Beltrami operator | invariant harmonic

Journal Article

Academie des Sciences. Comptes Rendus. Mathematique, ISSN 1631-073X, 10/2006, Volume 343, Issue 7, pp. 453 - 456

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of are defined using imbeddings into Lebesgue classes via radial derivatives. The...

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2011, Volume 15, Issue 1, pp. 101 - 127

We determine precise conditions for the boundedness of Bergman projections from Lebesgue classes onto the spaces in the title, which are members of the same...

Mathematical growth | Hermitian metric | Growth | BESOV-SPACES | Duality | Gleason problem | Lipschitz | ANALYTIC-FUNCTIONS | Zygmund | Decent functional | MATHEMATICS | Slice function | Boundary growth | Geodesic completeness | HOLOMORPHIC-FUNCTIONS | Taylor coefficient | Bergman projection | OPERATORS | Extremal point evaluation | Isometry | Kahler metric | Besov space | Laplace-Beltrami operator | Interpolation | alpha-Mobius invariance | Holomorphic sectional curvature | Bers | Bloch | Maximal space

Mathematical growth | Hermitian metric | Growth | BESOV-SPACES | Duality | Gleason problem | Lipschitz | ANALYTIC-FUNCTIONS | Zygmund | Decent functional | MATHEMATICS | Slice function | Boundary growth | Geodesic completeness | HOLOMORPHIC-FUNCTIONS | Taylor coefficient | Bergman projection | OPERATORS | Extremal point evaluation | Isometry | Kahler metric | Besov space | Laplace-Beltrami operator | Interpolation | alpha-Mobius invariance | Holomorphic sectional curvature | Bers | Bloch | Maximal space

Journal Article

06/2017

We evaluate integrals of certain polynomials over spheres and balls in real or complex spaces. We also promote the use of the Pochhammer symbol which gives the...

Mathematics - Complex Variables

Mathematics - Complex Variables

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 2002, Volume 50, Issue 3, pp. 649 - 664

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2002, Volume 342, Issue 1, pp. 163 - 186

Using reproducing kernel Hilbert spaces methods we develop a Schur-type algorithm for a subclass of the functions analytic and contractive in the ball. We also...

Unit ball | Leech's theorem | Schur algorithm | MATHEMATICS, APPLIED | unit ball

Unit ball | Leech's theorem | Schur algorithm | MATHEMATICS, APPLIED | unit ball

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2002, Volume 276, Issue 2, pp. 654 - 672

We solve Gleason's problem in the reproducing kernel Hilbert spaces with reproducing kernels 1/(1−∑ 1 Nz j w j) r for real r>0 and their counterparts for r⩽0,...

Reproducing kernel Hilbert space | Gleason's problem | Shift and resolvent | Homogeneous interpolation | Weighted Hardy space | Dirichlet-type space | Schur multiplier | Schur multiplier | shift and resolvent | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | homogeneous interpolation | INVARIANT SUBSPACES | weighted Hardy space | REPRODUCING KERNEL | reproducing kernel Hilbert space

Reproducing kernel Hilbert space | Gleason's problem | Shift and resolvent | Homogeneous interpolation | Weighted Hardy space | Dirichlet-type space | Schur multiplier | Schur multiplier | shift and resolvent | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | homogeneous interpolation | INVARIANT SUBSPACES | weighted Hardy space | REPRODUCING KERNEL | reproducing kernel Hilbert space

Journal Article

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