On the rate of growth of the means \(M_ p\) of holomorphic and pluriharmonic functions on bounded symmetric domains of \({\mathbb{C}}^ n\). (English) Zbl 0625.32003
The author considers holomorphic functions with bounded integral means on bounded symmetric domains of several complex variables. He obtains estimates on the fractional derivatives and integrals of such functions. This generalizes classical work of Hardy and Littlewood on the disc, and of Ian Graham and the reviewer on strongly pseudoconvex domains.
Reviewer: S.Krantz
MSC:
| 32A22 | Nevanlinna theory; growth estimates; other inequalities of several complex variables |
| 32A07 | Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010) |
| 32A35 | \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables |
| 31C10 | Pluriharmonic and plurisubharmonic functions |
Keywords:
Nevanlinna theory; Hardy spaces; holomorphic functions with bounded integral means on bounded symmetric domainsReferences:
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