Characterizations of Morrey type spaces

Sun, Fangmei ; Wulan, Hasi

Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 328-344

Résumé

For a nondecreasing function $K: [0, \infty)\rightarrow [0, \infty)$ and $0<s<\infty $, we introduce a Morrey type space of functions analytic in the unit disk $\mathbb {D}$, denoted by $\mathcal {D}^s_K$. Some characterizations of $\mathcal {D}^s_K$ are obtained in terms of K-Carleson measures. A relationship between two spaces $\mathcal {D}^{s_1}_K$ and $\mathcal {D}^{s_2}_K$ is given by fractional order derivatives. As an extension of some known results, for a positive Borel measure $\mu $ on $\mathbb {D}$, we find sufficient or necessary condition for the embedding map $I: \mathcal {D}^{s}_{K}\mapsto \mathcal {T}^s_{K}(\mu)$ to be bounded.

Détail

DOI : 10.4153/S0008439521000308

Mots-clés : Morrey type space, K-Carleson measure, embedding map, fractional order derivative