科研之友
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摘要
A conformal mapping f of the unit disk onto a Jordan domain G is considered. The boundary of G has the following structure. Another Jordan domain H is fixed whose boundary has Holder smoothness a > 1, and a countable family of open arcs dense in the boundary is specified. G is obtained by replacement of each of these distinguished arcs with a Holder arc of smoothness b, 1 < b < a, having the same end-points. Thus, G has Holder smoothness b. It is shown that if the lengths of the distinguished arcs decay sufficiently fast (depending on a and b), the function f still has Holder smoothness a on a set of positive measure on the unit circle. The numbers a and b are assumed to be nonintegers.
- 出版日期2016-10
