A note on weighted Bergman spaces and the Cesaro operator

Citation
G. Benke et Dc. Chang, A note on weighted Bergman spaces and the Cesaro operator, NAG MATH J, 159, 2000, pp. 25-43
Citations number
17
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
NAGOYA MATHEMATICAL JOURNAL
ISSN journal
0027-7630 → ACNP
Volume
159
Year of publication
2000
Pages
25 - 43
Database
ISI
SICI code
0027-7630(200009)159:<25:ANOWBS>2.0.ZU;2-C
Abstract
Let B denote the unit ball in C-n, and dV(z) normalized Lebesgue measure on B. For alpha > -1, define dV(alpha)(z) = (1- \z\(2))(alpha)dV(z). Let H(B) denote the space of holomorhic functions on B, and for 0 < p < infinity, l et A(p)(dV(alpha)) denote L-p(dV(alpha)) boolean AND H(B). In this note we characterize A(p)(dV(alpha)) as those functions in H(B) whose images under the action of a certain set of differential operators lie in L-p(dV(alpha)) . This is valid for 1 less than or equal to p < infinity. We also show that the Cesaro operator is bounded on A(p)(dV(alpha)) for 0 < p < infinity. An alogous results are given for the polydisc.