复空间的凸性与Hardy鞅不等式.pdf

401Q B B Vol.40, No. 1 1997M1c ACTA MATHEMATICA SINICA Jan., 1997 Hardy W (iCC i 430072) Turdebek N. Bekjan (CC GU 830046) kpPVzuDBanach TLrfcUn——Hardy AbvETLNlrioGmyZV Hardy q QCHd (1, 1) n (p, p ) nIi Φ HdAbsteXFVDTLNl q rRioA KgMhaOuDYjw Banach TLzNlHdI Brown xBFV hqSJ D Banach TLNlrio Hardy Brown xB MR(1991) 42, 60 O174, 0211 Inequalities of Hardy Martingales and Convexity in Complex Space Liu Peide (Department of Mathematics, Wuhan University, Wuhan 430072, China) (Fax: 027-7882661, E-mail: peide math. whcnc.ac.cn) Turdebek, N. Bekjan (Department of Mathematics, Xinjiang University, Urumuqi 830046, China) Abstract In this paper we study the relationships of inequalities of Hardy martingales with values in complex quasi-Banach space and analytic uniform convexity of the space, prove weak (1, 1), strong (p, p ) and convex Φ-function inequalities of q-mean-square function of Hardy martingales, and using them give characterizations of analytic q- uniform convexifiablity of complex space. In the same time we characterize the same property by using Banach-space-valued analytic functions and Brown motion in unit disk of complex plane. Keywords Complex quasi-Banach space, Analytic uniform convexity, Hardy martin- gale, Brown motion 1991 MR Subject Classification 42, 60 Chinese Library Classification O174, 0211 lIuCPIwfSsB swySZzXB fBkTWSzIugfWE hR 1994-12-28, YhR 1996-05-13, hR 1996-05-24 ecCuH 134 A