Projections, the weighted Bergman spaces, and the Bloch space
Author:
Boo Rim Choe
Journal:
Proc. Amer. Math. Soc. 108 (1990), 127136
MSC:
Primary 32A25; Secondary 32A40, 46E99, 47B38
MathSciNet review:
991692
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S00029939199009916920
PII:
S 00029939(1990)09916920
Keywords:
Projections,
weighted Bergman spaces,
Bloch space
Article copyright:
© Copyright 1990 American Mathematical Society
