Precise inclusion relations among Bergman-Besov and Bloch-Lipschitz spaces and H infinity on the unit ball of C-N


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KAPTANOĞLU H. T., ÜREYEN A. E.

MATHEMATISCHE NACHRICHTEN, vol.291, no.14-15, pp.2236-2251, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 291 Issue: 14-15
  • Publication Date: 2018
  • Doi Number: 10.1002/mana.201700236
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2236-2251
  • Keywords: atomic decomposition, Bergman, Besov, Bloch, Lipschitz space, bounded holomorphic function, Hadamard gap series, inclusion, Littlewood-Paley inequality, Ryll-Wojtaszczyk polynomial, Sobolev imbedding, PROJECTIONS, POLYNOMIALS, KERNELS, HARDY
  • Anadolu University Affiliated: No

Abstract

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 proofs. More importantly, we construct explicit functions in each space that show our relations are strict and the best possible. Many of our inclusions turn out to be sharper than the Sobolev imbeddings.