QK Spaces on the Unit Circle
We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight functions K1 and K2, K1≤K2, such that QK1(∂D)QK2(∂D)....
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/234790 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568237587431424 |
|---|---|
| author | Jizhen Zhou |
| author_facet | Jizhen Zhou |
| author_sort | Jizhen Zhou |
| collection | DOAJ |
| description | We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight functions K1 and K2, K1≤K2, such that QK1(∂D)QK2(∂D). We also prove that a measurable function belongs to QK(∂D) if and only if it is Möbius bounded in the Sobolev space LK2(∂D). Finally, we obtain a dyadic characterization of functions in QK(∂D) spaces in terms of dyadic arcs on the unit circle. |
| format | Article |
| id | doaj-art-abd6e16d41b540bca59e179852b35909 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-abd6e16d41b540bca59e179852b359092025-02-03T00:59:33ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/234790234790QK Spaces on the Unit CircleJizhen Zhou0School of Sciences, Anhui University of Science and Technology, Huainan, Anhui 232001, ChinaWe introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight functions K1 and K2, K1≤K2, such that QK1(∂D)QK2(∂D). We also prove that a measurable function belongs to QK(∂D) if and only if it is Möbius bounded in the Sobolev space LK2(∂D). Finally, we obtain a dyadic characterization of functions in QK(∂D) spaces in terms of dyadic arcs on the unit circle.http://dx.doi.org/10.1155/2014/234790 |
| spellingShingle | Jizhen Zhou QK Spaces on the Unit Circle Journal of Function Spaces |
| title | QK Spaces on the Unit Circle |
| title_full | QK Spaces on the Unit Circle |
| title_fullStr | QK Spaces on the Unit Circle |
| title_full_unstemmed | QK Spaces on the Unit Circle |
| title_short | QK Spaces on the Unit Circle |
| title_sort | qk spaces on the unit circle |
| url | http://dx.doi.org/10.1155/2014/234790 |
| work_keys_str_mv | AT jizhenzhou qkspacesontheunitcircle |