The equivalent norms of F(p,q,s) space in C<

Abstract

Equivalent normUnit ball a b s t r a c tCharacterizing functions in the F (p, q, s) space is work of considerable interest nowadays. In this paper we give six equivalent norms of the functions in the F (p, q, s) space on the unit ball in C n under different conditions.  and g(z, a) = log 1 |ϕ a (z)| .

On F(p, q, s) Spaces

“…The following result by Zhang, He and Cao [67] gives some characterizations of F (p, q, s) on the unit ball in C n : Theorem 9.17 Let 0 < p < ∞, 0 ≤ s < ∞, −n − 1 < q < ∞ and q + s > −1. The following quantities are equivalent:…”

$\mathcal N(p, q, s)$-type spaces in the unit ball of $\mathbb C^n$(III): various characterizations

“…An alternative proof of the equivalence of (i), (ii), (iii) and (iv) in Corollary 3.5 can be found in [9], which depends on a careful estimate of…”

$N(p, q, s)$-type spaces in the unit ball of $C^n$

“…and an f ∈ H(B) is said to belong to the F 0 (p, q, t)-space if The F (p, q, t)-spaces were first introduced by R. Zhao on the unit disk in C in [42], and later studied on the unit disk and the unit ball B of C n by various authors (see, e.g, [17,29,40,41] and the reference therein). However, to the best of our knowledge, currently there are few results in the theory of F (p, q, t)-spaces in the unit ball due to the complexity of the parameters p, q and t, as well as the high dimension.…”