The growth of derivatives of multipliers of fractional Cauchy transforms

[摘要] In this paper we prove a number of sharp results on the permissible growth of derivatives of multipliers of fractional Cauchy transforms. For example, we prove that if f is an element of M-1 then there exists a positive constant C such that integral(-pi)(pi)\f'(re(i theta))\d theta less than or equal to C\\f\\(M1)1/1-r 1/1+log(1/(1-r)) for r is an element of [0, 1). This result is proved to be sharp. (C) 1997 Academic Press.

[发布日期] 1997-08-15