Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions
Let D be the unit disc of complex plane C, and H=Hol(D) the class of functions analytic in D. Recall that an f∈Hol(D) is said to belong to the Bloch space B=B(D) if ‖f‖_{B}:=sup_{z∈D}(1-|z|²)|f′(z)|<+∞. With the norm ‖f‖=|f(0)|+‖f‖_{B}, B is Banach space. Let B₀=B₀(D) be the Bloch space which co...
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| Format: | Article |
| Language: | English |
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Elsevier
2016-08-01
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| Series: | Kuwait Journal of Science |
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| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/1020 |
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| author | Mübariz T. Garayev Mehmet Gürdal Ulaş Yamancı |
| author_facet | Mübariz T. Garayev Mehmet Gürdal Ulaş Yamancı |
| author_sort | Mübariz T. Garayev |
| collection | DOAJ |
| description | Let D be the unit disc of complex plane C, and H=Hol(D) the class of functions analytic in D. Recall that an f∈Hol(D) is said to belong to the Bloch space B=B(D) if
‖f‖_{B}:=sup_{z∈D}(1-|z|²)|f′(z)|<+∞.
With the norm ‖f‖=|f(0)|+‖f‖_{B}, B is Banach space. Let B₀=B₀(D) be the Bloch space which consists of all f∈B satisfying
lim_{|z|→1}(1-|z|²)|f′(z)|=0.
Here we give a new description of Bloch spaces and weighted Bergman spaces in terms of Berezin symbols of diagonal operators associated with the Taylor coefficients of their functions. We also give in terms of Berezin symbols a characterization of the multiple shift invariant subspaces of these Bloch spaces. Some other questions are also discussed. |
| format | Article |
| id | doaj-art-25af08da129e4db9bcd394f9aeeea8d3 |
| institution | Kabale University |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2016-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-25af08da129e4db9bcd394f9aeeea8d32025-08-20T03:24:56ZengElsevierKuwait Journal of Science2307-41082307-41162016-08-01433365Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questionsMübariz T. Garayev0Mehmet Gürdal1Ulaş Yamancı2Dept. of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDept. of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, Isparta, TurkeyDept. of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, Isparta, TurkeyLet D be the unit disc of complex plane C, and H=Hol(D) the class of functions analytic in D. Recall that an f∈Hol(D) is said to belong to the Bloch space B=B(D) if ‖f‖_{B}:=sup_{z∈D}(1-|z|²)|f′(z)|<+∞. With the norm ‖f‖=|f(0)|+‖f‖_{B}, B is Banach space. Let B₀=B₀(D) be the Bloch space which consists of all f∈B satisfying lim_{|z|→1}(1-|z|²)|f′(z)|=0. Here we give a new description of Bloch spaces and weighted Bergman spaces in terms of Berezin symbols of diagonal operators associated with the Taylor coefficients of their functions. We also give in terms of Berezin symbols a characterization of the multiple shift invariant subspaces of these Bloch spaces. Some other questions are also discussed.https://journalskuwait.org/kjs/index.php/KJS/article/view/1020Berezin symbolBloch spacediagonal operatorinvariant subspaceweighted Bergman space. |
| spellingShingle | Mübariz T. Garayev Mehmet Gürdal Ulaş Yamancı Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions Kuwait Journal of Science Berezin symbol Bloch space diagonal operator invariant subspace weighted Bergman space. |
| title | Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions |
| title_full | Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions |
| title_fullStr | Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions |
| title_full_unstemmed | Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions |
| title_short | Description of Bloch spaces, weighted Bergman spaces and invariant subspaces, and related questions |
| title_sort | description of bloch spaces weighted bergman spaces and invariant subspaces and related questions |
| topic | Berezin symbol Bloch space diagonal operator invariant subspace weighted Bergman space. |
| url | https://journalskuwait.org/kjs/index.php/KJS/article/view/1020 |
| work_keys_str_mv | AT mubariztgarayev descriptionofblochspacesweightedbergmanspacesandinvariantsubspacesandrelatedquestions AT mehmetgurdal descriptionofblochspacesweightedbergmanspacesandinvariantsubspacesandrelatedquestions AT ulasyamancı descriptionofblochspacesweightedbergmanspacesandinvariantsubspacesandrelatedquestions |