Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C
We study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general L1 symbols and compactness of bounded operators on the Bergman spaces with constant exponents...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/1417989 |
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| _version_ | 1832564528913580032 |
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| author | Dieudonne Agbor |
| author_facet | Dieudonne Agbor |
| author_sort | Dieudonne Agbor |
| collection | DOAJ |
| description | We study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general L1 symbols and compactness of bounded operators on the Bergman spaces with constant exponents can readily be extended to the variable exponent setting. In particular, if S is a finite sum of finite products of Toeplitz operators with symbols from class BT, then S is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disc. |
| format | Article |
| id | doaj-art-3fff4636169f4d3eaa35df6d79181da1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3fff4636169f4d3eaa35df6d79181da12025-02-03T01:10:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/14179891417989Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of CDieudonne Agbor0Department of Mathematics, Faculty of Science, University of Buea, P.O. Box 63, Buea, CameroonWe study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general L1 symbols and compactness of bounded operators on the Bergman spaces with constant exponents can readily be extended to the variable exponent setting. In particular, if S is a finite sum of finite products of Toeplitz operators with symbols from class BT, then S is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disc.http://dx.doi.org/10.1155/2018/1417989 |
| spellingShingle | Dieudonne Agbor Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C International Journal of Mathematics and Mathematical Sciences |
| title | Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C |
| title_full | Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C |
| title_fullStr | Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C |
| title_full_unstemmed | Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C |
| title_short | Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C |
| title_sort | compact operators on the bergman spaces with variable exponents on the unit disc of c |
| url | http://dx.doi.org/10.1155/2018/1417989 |
| work_keys_str_mv | AT dieudonneagbor compactoperatorsonthebergmanspaceswithvariableexponentsontheunitdiscofc |