International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 611-612

Fractional derivatives of holomorphic functions on bounded symmetric domains of Cn

Zengjian Lou

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.


Let fH(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 fAs,t,α(Bn), and fs,t,αCf|β|p,q,α, s=δpδβ, t=δqδβ

(II) If β=α+1p+nq, then fB(Bn) and fBCf|β|p,q,α

(III) If β>α+1p+nq, then fΛβα+1pnq(Bn) especially If β=1 then fΛ1α+1pnqCf|1|p,q,α where Bn is the unit ball of Cn.