Analytic Campanato Spaces and Their Compositions

The pseudoanalytic extensions for some spaces of analytic functions

“…Recently, the interest in analytic Morrey space has grown rapidly. See [8,18,20,21,23,31,32] for more results of L 2,λ spaces. Note that if f ∈ L 2,λ , then its primitive function F belongs to H 2 .…”

Holomorphic Campanato spaces on the unit ball

“…When n = 1, some fundamental function/operator-theoretic properties of HC s have been discovered in [29,41,43,46,49,50]. However, when n > 1, as far as we know, there is only one paper partially touching this holomorphic space -more precisely - [11] has established the corona and multiplication theorems for HC s under s ∈ (0, n/2) extending the cases s ∈ (−1, 0) (cf.…”

Two Predualities and Three Operators over Analytic Campanato Spaces

“…The following table tells us that how CA p looks like (see, e.g. [29,30,31] and their references): Index p Analytic Campanato Space CA p p ∈ (−∞, 0] Analytic Hardy space H 2 p ∈ (0, 1) Holomorphic Morrey space H 2,p p = 1 Analytic John-Nirenberg space BMOA p ∈ (1,3] Analytic Lipschitz space A p−1…”

“…Continuing essentially from [29, 2, Chapter 3], [30,31] and [9,18,27], in this paper we study two predualities and three operators associated to the analytic Campanato spaces. More precisely, in §2 we use §2.1 -the Choquet integrals and quadratic tent spaces to discover §2.2 -the predual space of CA p and §2.3 -the dual space of CA 0,p .…”