Weighted Harmonic Bloch Spaces on the Ball

Dogan O. F., ÜREYEN A. E.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.12, no.5, pp.1143-1177, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1007/s11785-017-0645-9
  • Journal Name: COMPLEX ANALYSIS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1143-1177
  • Keywords: Harmonic Bloch space, Bergman space, Reproducing kernel, Radial fractional derivative, Bergman projection, Duality, Gleason problem, Atomic decomposition, Oscillatory characterization, UNIT BALL, BESOV-SPACES, REPRODUCING KERNELS, BERGMAN PROJECTIONS, LIPSCHITZ
  • Anadolu University Affiliated: No

Abstract

We study the family of weighted harmonic Bloch spaces , on the unit ball of . We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that are more compatible with reproducing kernels of harmonic Bergman-Besov spaces. We consider a class of integral operators related to harmonic Bergman projection and determine precisely when they are bounded on . We define projections from to and as a consequence obtain integral representations. We solve the Gleason problem and provide atomic decomposition for all . Finally we give an oscillatory characterization of when -1.