A note on a space Hp, a of holomorphic functions

Publisher： Cambridge University Press

E-ISSN： 1755-1633|35|3|471-479

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.35, Iss.3, 1987-06, pp. : 471-479

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Abstract

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

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