| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4668727 | Bulletin des Sciences Mathématiques | 2016 | 13 Pages |
Abstract
By proving a converse to a theorem of Salem and Zygmund the paper gives a full description of the sets E of points x where the integral ∫01(F(x+t)−F(x−t))/tdt is infinite for a continuous and nondecreasing function F. It is shown that for this it is necessary and sufficient that E is a GδGδ set of zero logarithmic capacity. Several corollaries are derived concerning boundary values of univalent functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Arthur A. Danielyan, Vilmos Totik,