Representations and interpolations of harmonic Bergman functions on half-spaces

DOI10.1017/S0027763000025174zbMath0954.31004OpenAlexW1573811416MaRDI QIDQ4236908

HeungSu Yi, Boo Rim Choe

Publication date: 14 February 2001

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000025174

zbMATH Keywords

little Bloch spacesBergman metric ballsdistance estimates to the harmonic little Bloch spacepseudohyperbolic ballsuniqueness theorem for harmonic Bergman functions

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Normal functions of one complex variable, normal families (30D45) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

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Finite rank product theorems for Toeplitz operators on the half-space ⋮ Positive Schatten(-Herz) class Toeplitz operators on the half-space ⋮ On boundedness of Bergman projection operators in Banach spaces of holomorphic functions in half-plane and harmonic functions in half-space ⋮ Harmonic Bergman spaces on the real hyperbolic ball: atomic decomposition, interpolation and inclusion relations ⋮ Difference of composition operators on the weighted Bergman spaces over the half-plane ⋮ On an interpolation problem for the classical weighted harmonic Bergman space ⋮ Interpolating sequences of parabolic Bergman spaces ⋮ Difference of composition operators over the half-plane ⋮ Difference of composition operators over the half-plane ⋮ Path components of composition operators over the half-plane ⋮ Representations and interpolations of weighted harmonic Bergman functions ⋮ Double integral characterizations of harmonic Bergman spaces ⋮ Carleson inequalities on parabolic Bergman spaces ⋮ Harmonic Bergman functions as radial derivatives of Bergman functions

Cites Work

• Interpolation by functions in Bergman spaces
• Fractional derivatives of Bloch functions, growth rate, and interpolation
• Interpolating sequences for the derivatives of Bloch functions
• Suites D'Interpolation Pour les Classes de Bergman de la Boule et du Polydisque de Cⁿ
• Harmonic Bergman Functions on Half-Spaces