Abstract
In this paper, we introduce a class of holomorphic Banach spaces NK of functions on the unit ball B of Cn. We develop the necessary and sufficient condition for NK(B) spaces to be non-trivial and we discuss the nesting property of NK(B) spaces. Also, we obtain some characterizations of functions with Hadamard gaps in NK(B) spaces. As a consequence, we prove a necessary and sufficient condition for that NK(B) spaces coincides with the Beurling-type space.
Highlights
IntroductionFor a ∈ the Möbius invariant Green function in the unit ball denoted by G ( z, a) = g (φa (z)) where g ( z) is defined by:
For any z = ( z1, z= 2, zn ), w ( w1, w2, wn ) ∈ n, the inner product is de-( ) fined by z, w = z1 w1 z2 w2, zn wn, and write z= z, w .Let dv be the Lebesgue volume measure on n, normalized so that v ( ) ≡ 1 and dσ be the surface measure on
We introduce K ( ) spaces, in terms of the right continuous and non-decreasing function K : (0, ∞) → [0, ∞) on the unit ball
Summary
For a ∈ the Möbius invariant Green function in the unit ball denoted by G ( z, a) = g (φa (z)) where g ( z) is defined by:. Let K : (0, ∞) → [0, ∞) is a right-continuous, non-decreasing function and is not equal to zero identically. Hadamard gaps series and Hadamard product on K spaces of holomorphic function in the case of the unit disk has been studied quite well in [4] and [5]. Paper, given two quantities Af and Bf both depending on a function f ∈ ( ) , we are going to write Af Bf if there exists a constant. We introduce K ( ) spaces, in terms of the right continuous and non-decreasing function K : (0, ∞) → [0, ∞) on the unit ball. We show that the sufficient condition is a necessary to
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