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Original Articles

Biharmonic Bergman space and its reproducing kernel

Pages 1642-1663 | Received 25 Jan 2016, Accepted 07 Nov 2017, Published online: 07 Dec 2017

References

  • Nicolescu M . Les fonctions polyharmoniques. Paris: Hermann & Cie; 1936.
  • Miao J . Toeplitz operators on harmonic Bergman spaces. Integral Equ Oper Theory. 1997;27:426–438.
  • Stroethoff K . Compact Toeplitz operators on weighted harmonic Bergman spaces. J Aust Math Soc. 1998;64:136–148.
  • Zhao ZG . The harmonic Bergman kernels for punctured domains. Acta Math Sin (Engl Ser). 2014;30:1977–1988.
  • Pavlović M . Decompositions of Lp and Hardy spaces of polyharmonic functions. J Math Anal Appl. 1997;216:499–509.
  • Pessoa LV . On the structure of polyharmonic Bergman type spaces over the unit disk. Complex Var Elliptic Equ. 2015;60:1668–1684.
  • Pessoa LV . True poly-Bergman and poly-Bergman kernels for the complement of a closed disk. Complex Anal Oper Theory. 2013;7(5):1569–1581.
  • Nishio M , Tanaka K . Harmonic Bergman kernels and Toeplitz operators on the ball with radial measures. Rev Roumaine Math Pures Appli. 2017;62:155–169.
  • Coifman R , Rochberg R . Representation theorems for holomorphic and harmonic functions in Lp . Astérisque. 1980;77:1–66.
  • Aronszajn N , Creese TM , Lipkin LJ . Polyharmonic functions. Oxford: Clarendon press; 1983.
  • Axler S , Bourdon P , Ramey W . Harmonic function theory. New York (NY): Springer-Verlag; 1992.
  • Futamura T , Kishi K , Mizuta Y . A generalization of Bôcher’s theorem for polyharmonic functions. Hiroshima Math J. 2001;31:59–70.
  • Hsu SY . Removable singularity of the polyharmonic equation. Nonlinear Anal. 2010;72:624–627.

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