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Generalized Area Operators on Hardy Spaces

✍ Scribed by William S. Cohn

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
183 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

We show that if 0p -ϱ then the operator Gf s H f z dr 1 y z ⌫Ž . p p Ž < <. maps the Hardy space H to L d if and only if is a Carleson measure.

Ž . Here ⌫ is the usual nontangential approach region with vertex on the unit

and d is arclength measure on the circle. We also show that if 0p F 1, ␤ ) 0, and 1 y ␤ p ) 0 then the operator p p Ž < <. Gf maps the Hardy᎐Sobolev space H into L d if and only if the function ␤ Ž . Ž < <. p, 1y␤ p G s H dr 1 y z belongs to the Morrey space L . In case p s 1, ⌫Ž .

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