Characterizations of Morrey type spaces
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 meas...
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| Published in | Canadian mathematical bulletin Vol. 65; no. 2; pp. 328 - 344 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Canada
Canadian Mathematical Society
01.06.2022
Cambridge University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0008-4395 1496-4287 |
| DOI | 10.4153/S0008439521000308 |
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| 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. |
|---|---|
| AbstractList | For a nondecreasing function $K: [0, \infty)\rightarrow [0, \infty)$ and $0<\infty $<="" tex-math=""><\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. 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. 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. |
| Author | Wulan, Hasi Sun, Fangmei |
| Author_xml | – sequence: 1 givenname: Fangmei surname: Sun fullname: Sun, Fangmei email: 18fmsun@stu.edu.cn organization: Department of Mathematics, Shantou University, Shantou 515063, People’s Republic of China e-mail: 18fmsun@stu.edu.cn – sequence: 2 givenname: Hasi surname: Wulan fullname: Wulan, Hasi email: wulan@stu.edu.cn organization: Department of Mathematics, Shantou University, Shantou 515063, People’s Republic of China e-mail: 18fmsun@stu.edu.cn |
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| Cites_doi | 10.4171/RMI/326 10.1090/S0002-9947-1938-1501936-8 10.1080/17476930701272764 10.5802/aif.1509 10.1016/0022-1236(69)90022-6 10.5186/aasfm.2013.3801 10.1016/j.jfa.2005.07.004 10.1007/s00020-005-1391-3 10.1002/mana.201300301 10.1016/j.jmaa.2012.12.052 10.1080/17476933.2018.1549036 10.1090/S0002-9939-1986-0861756-X 10.1006/jfan.1999.3490 10.1016/S0022-1236(03)00020-X 10.1007/s11425-014-4811-5 10.1090/surv/138 10.1090/S0002-9947-1988-0957062-1 10.1007/s12220-016-9708-9 10.1007/s00209-008-0338-1 10.2307/1970375 10.1007/s00020-014-2124-2 10.1016/j.aim.2007.08.015 |
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| Keywords | Morrey type space 30D99 47B38 fractional order derivative embedding map 30H25 K-Carleson measure 30D45 |
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| Snippet | 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... For a nondecreasing function $K: [0, \infty)\rightarrow [0, \infty)$ and $0<\infty $<="" tex-math=""><\infty>, we introduce a Morrey type space of functions... |
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| SubjectTerms | Fractional calculus Mathematical analysis Partial differential equations |
| Title | Characterizations of Morrey type spaces |
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