Mulholland proved several interesting results for Dirichlet series and related integrals. A few of these results have been
recently generalized. The aim of the present paper is to improve further these theorems and to prove certain converse statements.
Finally, we show that our theorems cannot be improved any longer.
P. L. Ul'yanov has recently proved a new type of equivalence theorems in connection with the classical equivalence theorem
by A. Plessner. Making use of certain results proved by us more than thirty years ago, we extend Ul'yanov's results into more
general equivalence theorems.
The factorization of inequalities for infinite numerical series is a new research field. A monograph giving a systematic treatment of this subject is due to BENNETT. Here two theorems of this type are proved. Our new results extend previous theorems to the so-called Mulholland functions.
Получено восемь нера венств для квазимоно тонных последовательносте й (и восемь неравенств для функций). Эти нерав енства в определенно м смысле могут рассматривать ся как обращение известных неравенств Харди-Лит тлвуда.