Projections, the weighted Bergman spaces, and the Bloch space

Author:
Boo Rim Choe

Journal:
Proc. Amer. Math. Soc. **108** (1990), 127-136

MSC:
Primary 32A25; Secondary 32A40, 46E99, 47B38

DOI:
https://doi.org/10.1090/S0002-9939-1990-0991692-0

MathSciNet review:
991692

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Abstract | References | Similar Articles | Additional Information

Abstract: It has been known that there is a family of projections of the Lebesgue spaces onto the Bergman spaces on the unit ball of . The corresponding result for the weighted Bergman spaces is obtained. As applications a solution of Gleason's problem at the origin for and a characterization of in terms of partial derivatives are indicated without proof. Also the natural limiting case is found: , the Bloch space, and , the little Bloch space. Moreover, simple bounded linear operators , with , are found so that is the identity on . As an application the dualities and are established under each of pairings suggested by projections .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-0991692-0

Keywords:
Projections,
weighted Bergman spaces,
Bloch space

Article copyright:
© Copyright 1990
American Mathematical Society