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On Some Lebesgue and Hardy Vector Classes

Najafov T.I. and Sadigova S.R.

Vector classes Lp (X) and Hp (X) are considered, where X is a Banach space. These classes are the generalizations of similar Lebesgue and Hardy classes in scalar case. Two different definitions for Hardy class are given, and their equivalence is proved. Riemann boundary value problems in different formulations are considered. Under certain conditions, their correct solvability is proved. Subspace bases in Lp (X) are also considered. An abstract analogue of the ”1/4-Kadets” theorem is obtained.