Article contents
Characterizations of Morrey type spaces
Published online by Cambridge University Press: 14 May 2021
Abstract
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.
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- © Canadian Mathematical Society 2021
Footnotes
This research is supported by the National Natural Science Foundation of China (Grant Number 11720101003)
References
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