METRIC CHARACTERISTICS OF EXCEPTIONAL SETS ARISING IN ESTIMATES OF SUBHARMONIC FUNCTIONS
Vladimir Eiderman · Sbornik Mathematics · 1995
The classes of subharmonic functions , , , of finite proximate order are considered, which generalize the class of functions of the form , where is an entire function of completely regular growth in the sense of Levin-Pfluger. Estimates are obtained for the exceptional sets for functions containing the centers and radii of the balls covering . Coverings of various structures are studied. In particular, the following problem is solved: Under what conditions on a continuous increasing function , , , can the set be covered by balls such that as ? In an approach proposed by V. S. Azarin these problems reduce to studying the connection between convergence in the topology of the space of generalized functions and convergence outside the exceptional sets.Bibliography: 14 titles.