Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Abstract:
Let denote the open unit disc, and let denote the disc algebra. The subsets of such that the inclusion holds for every nonconstant continuous on , or the inclusion holds for every bounded harmonic nonholomorphic function on continuous on , are characterized. In the first case the condition is that has positive measure, and in the second case that has full measure in .