International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 611-612
doi:10.1155/S0161171296000853
Fractional derivatives of holomorphic functions on bounded symmetric domains of Cn
Department of Mathematics, Qufu Normal University, Qufu Shandong, 273165, China
Received 8 March 1994; Revised 13 January 1995
Copyright © 1996 Zengjian Lou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let f∈H(Bn). f|β| denotes the βth fractional derivative of f. If f|β|∈Ap,q,α(Bn), we show that
(I) β<α+1p+nq=δ, then f∈As,t,α(Bn), and ‖f‖s,t,α≤C‖f|β|‖p,q,α, s=δpδ−β, t=δqδ−β
(II) If β=α+1p+nq, then f∈B(Bn) and ‖f‖B≤C‖f|β|‖p,q,α
(III) If β>α+1p+nq, then f∈Λβ−α+1p−nq(Bn) especially If β=1 then ‖f‖Λ1−α+1p−nq≤C‖f|1|‖p,q,α where Bn is the unit ball of Cn.