Analytic Campanato Spaces and Their Compositions

Abstract

This paper is devoted to characterizing the analytic Campanato spaces AL p,η (including the analytic Morrey spaces, the analytic John-Nirenberg space, and the analytic Lipschitz/Hölder spaces) on the complex unit disk D in terms of the Möbius mappings and the Littlewood-Paley forms, and consequently their compositions with the analytic self-maps of D.

Analytic Morrey Spaces and Bloch-Type Spaces

“…When ( ) ≡ 1, the result reduces to Xiao and Yuan in [15]. When ( ) ≡ , , denote the multiplication operator.…”

A family of Dirichlet–Morrey spaces

“…Morrey spaces were introduced in the 1930's in connection to partial differential equations, and were subsequently studied as function classes in harmonic analysis on Euclidean spaces. The analytic Morrey spaces were introduced recently and studied by several authors, see for example [18], [22], [23] and [11].…”

Holomorphic Campanato spaces on the unit ball

“…When , some fundamental function/operator‐theoretic properties of have been discovered in , , , , , . However, when , to the best of our knowledge, there is only one paper partially touching this holomorphic space–more precisely– has established the corona and multiplication theorems for under extending the cases (cf.…”

“…HC s and enjoys the following structure table (see, e.g. [8, 7, 11, 16, 17 and 19, p. 209-217] for the real counterparts which are often used in the theory of elliptic partial differential equations): When n = 1, some fundamental function/operator-theoretic properties of HC s have been discovered in [20], [31], [32], [35], [37], [38]. However, when n > 1, to the best of our knowledge, there is only one paper partially touching this holomorphic space-more precisely- [9] has established the corona and multiplication theorems for HC s under s ∈ (0, n/2) extending the cases s ∈ (−1, 0) (cf.…”