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Bergman Projections and Operators on Hardy Spaces

✍ Scribed by William S. Cohn

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
957 KB
Volume
144
Category
Article
ISSN
0022-1236

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✦ Synopsis

We show that Toeplitz like'' operators of the form T s u f=P s (uf ), where P s is a weighted Bergman projection, are bounded on the Hardy spaces H p , for 1 p< for certain symbols'' u defined on the unit disk. In particular, T s u is bounded if u is of the form u=h+G+ where h is a bounded harmonic function and G+ is the Green potential of a Borel measure + satisfying the condition that (1& |z|) d+(z) is a Carleson measure. If u is of the form u=h+G+ where + is a positive measure then these two conditions are also necessary that T s u be bounded on H p . We also consider the cases 0< p<1.

1997 Academic Press a (dm s ). For s>0 let z=re i% be a point in the unit disk and let dm s be the measure dm s (z)=(sÂ?)(1&r 2 ) s&1 dm(z), where dm is two dimensional Lebesgue measure. L p (dm s ) will denote the Lebesgue space of measurable functions defined on the unit disk integrable with respect to dm s and article no. FU962991

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