Toeplitz operators with BMO symbols and the Berezin transform
We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L∞ fun...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203212035 |
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| _version_ | 1832562906468712448 |
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| author | Nina Zorboska |
| author_facet | Nina Zorboska |
| author_sort | Nina Zorboska |
| collection | DOAJ |
| description | We prove that the boundedness and compactness of the Toeplitz
operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin
transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L∞ function. |
| format | Article |
| id | doaj-art-ca86e53a0f494aa5864367ee3bca9347 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ca86e53a0f494aa5864367ee3bca93472025-02-03T01:21:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003462929294510.1155/S0161171203212035Toeplitz operators with BMO symbols and the Berezin transformNina Zorboska0Department of Mathematics, University of Manitoba, Winnipeg, Manitobia R3T 2N2, CanadaWe prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L∞ function.http://dx.doi.org/10.1155/S0161171203212035 |
| spellingShingle | Nina Zorboska Toeplitz operators with BMO symbols and the Berezin transform International Journal of Mathematics and Mathematical Sciences |
| title | Toeplitz operators with BMO symbols and the Berezin transform |
| title_full | Toeplitz operators with BMO symbols and the Berezin transform |
| title_fullStr | Toeplitz operators with BMO symbols and the Berezin transform |
| title_full_unstemmed | Toeplitz operators with BMO symbols and the Berezin transform |
| title_short | Toeplitz operators with BMO symbols and the Berezin transform |
| title_sort | toeplitz operators with bmo symbols and the berezin transform |
| url | http://dx.doi.org/10.1155/S0161171203212035 |
| work_keys_str_mv | AT ninazorboska toeplitzoperatorswithbmosymbolsandtheberezintransform |