Sets of uniqueness for regular methods of summation

Any set of uniqueness for regular method of summation for trigonometric series is also a set of uniqueness. J. Marcinkiewicz and A. Zygmund constructed regular method of summation for that there not exist sets of uniqueness. We formulate some open questions and results on relation between sets of uniqueness and sets of uniqueness for regular methods of summation. In particular: if an empty set is a set of uniqueness for regular method of summation T then every set of uniqueness for trigonometric series that is both a Gδ and an Fσ is also a set of uniqueness for method T .