Functions of Omega-Bounded Type

The book gives the basic results of the theory of the spaces A^pω of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ω permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian''s theory of spaces A^pα (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the ω-extensions of M. M. Djrbashian''s two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane.