Singular Integral Operators with Bergman–Besov Kernels on the Ball

  • H. Turgay KaptanoğluEmail author
  • A. Ersin Üreyen


We completely characterize in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by Bergman–Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of \({\mathbb {C}}^N\). The integral operators generalize the Bergman–Besov projections. To find the necessary conditions for boundedness, we employ a new versatile method that depends on precise imbedding and inclusion relations among various holomorphic function spaces. The sufficiency proofs are by Schur tests or integral inequalities.


Integral operator Bergman–Besov kernel Bergman–Besov space Bloch–Lipschitz space Bergman–Besov projection Radial fractional derivative Schur test Forelli–Rudin estimate Inclusion relation 

Mathematics Subject Classification

Primary 47B34 47G10 Secondary 32A55 45P05 46E15 32A37 32A36 30H25 30H20 



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Authors and Affiliations

  1. 1.Bilkent Üniversitesi, Matematik BölümüAnkaraTurkey
  2. 2.Eskişehir Teknik Üniversitesi, Fen Fakültesi Matematik BölümüEskisehirTurkey

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