### Abstract

It has been known that there is a family of projections P_{s} of the Lebesgue spaces onto the Bergman spaces on the unit ball of ℂ_{n}(n ≥ 1). The corresponding result for the weighted Bergman spaces A^{p}α is obtained. As applications a solution of Gleason’s problem at the origin for Apa and a characterization of A^{p}α in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: P_{s}L^{∞} = S, the Bloch space, and P_{s}L^{∞} = B the P_{s}C_{0} Bloch space. Moreover, simple bounded linear operators L_{s}: B →s L^{∞} B = (A^{1}α)* and B_{0}* = A^{1}α are established under each of pairings suggested by projections P_{s}.

Original language | English |
---|---|

Pages (from-to) | 127-136 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 108 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bloch space
- Projections
- Weighted Bergman spaces

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Projections, the weighted bergman spaces, and the bloch space.** / Choe, Boo Rim.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 108, no. 1, pp. 127-136. https://doi.org/10.1090/S0002-9939-1990-0991692-0

}

TY - JOUR

T1 - Projections, the weighted bergman spaces, and the bloch space

AU - Choe, Boo Rim

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

KW - Bloch space

KW - Projections

KW - Weighted Bergman spaces

UR - http://www.scopus.com/inward/record.url?scp=84966251834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966251834&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1990-0991692-0

DO - 10.1090/S0002-9939-1990-0991692-0

M3 - Article

AN - SCOPUS:84966251834

VL - 108

SP - 127

EP - 136

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -