Fractional derivatives of holomorphic functions on bounded symmetric domains of C n

Zengjian Lou

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-2

Abstract:

Let f ∈ H ( B n ) . f | β | denotes the β t h fractional derivative of f . If f | β | ∈ A p , q , α ( B n ) , we show that

(I) β < α + 1 p + n q = δ , then f ∈ A s , t , α ( B n ) , and ‖ f ‖ s , t , α ≤ C ‖ f | β | ‖ p , q , α , s = δ p δ − β , t = δ q δ − β

(II) If β = α + 1 p + n q , then f ∈ B ( B n ) and ‖ f ‖ B ≤ C ‖ f | β | ‖ p , q , α

(III) If β > α + 1 p + n q , then f ∈ Λ β − α + 1 p − n q ( B n ) especially If β = 1 then ‖ f ‖ Λ 1 − α + 1 p − n q ≤ C ‖ f | 1 | ‖ p , q , α where B n is the unit ball of C n .

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:746234

DOI: 10.1155/S0161171296000853

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