Projections, the weighted bergman spaces, and the bloch space

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Abstract

It has been known that there is a family of projections Ps of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂn(n ≥ 1). The corresponding result for the weighted Bergman spaces Apα is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of Apα in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: PsL = S, the Bloch space, and PsL = B the PsC0 Bloch space. Moreover, simple bounded linear operators Ls: B →s L B = (A1α)* and B0* = A1α are established under each of pairings suggested by projections Ps.

Original languageEnglish
Pages (from-to)127-136
Number of pages10
JournalProceedings of the American Mathematical Society
Volume108
Issue number1
DOIs
Publication statusPublished - 1990
Externally publishedYes

Keywords

  • Bloch space
  • Projections
  • Weighted Bergman spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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