Boundary behaviour of analytic functions in spaces of Dirichlet type
<p/> <p>For <inline-formula><graphic file="1029-242X-2006-92795-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-92795-i2.gif"/></inline-formula>, we let <inline-formula><graphic file="1029-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2006/927957 |
| _version_ | 1818912398445117440 |
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| author | Peláez José Ángel Girela Daniel |
| author_facet | Peláez José Ángel Girela Daniel |
| author_sort | Peláez José Ángel |
| collection | DOAJ |
| description | <p/> <p>For <inline-formula><graphic file="1029-242X-2006-92795-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-92795-i2.gif"/></inline-formula>, we let <inline-formula><graphic file="1029-242X-2006-92795-i3.gif"/></inline-formula> be the space of all analytic functions <inline-formula><graphic file="1029-242X-2006-92795-i4.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-92795-i5.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2006-92795-i6.gif"/></inline-formula> belongs to the weighted Bergman space <inline-formula><graphic file="1029-242X-2006-92795-i7.gif"/></inline-formula>. We obtain a number of sharp results concerning the existence of tangential limits for functions in the spaces <inline-formula><graphic file="1029-242X-2006-92795-i8.gif"/></inline-formula>. We also study the size of the exceptional set <inline-formula><graphic file="1029-242X-2006-92795-i9.gif"/></inline-formula>, where <inline-formula><graphic file="1029-242X-2006-92795-i10.gif"/></inline-formula> denotes the radial variation of <inline-formula><graphic file="1029-242X-2006-92795-i11.gif"/></inline-formula> along the radius <inline-formula><graphic file="1029-242X-2006-92795-i12.gif"/></inline-formula>, for functions <inline-formula><graphic file="1029-242X-2006-92795-i13.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-19T23:13:58Z |
| format | Article |
| id | doaj.art-ab22acd8347e47888df1f71a86c2c12d |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-19T23:13:58Z |
| publishDate | 2006-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ab22acd8347e47888df1f71a86c2c12d2022-12-21T20:02:08ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2006-01-0120061927957Boundary behaviour of analytic functions in spaces of Dirichlet typePeláez José ÁngelGirela Daniel<p/> <p>For <inline-formula><graphic file="1029-242X-2006-92795-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-92795-i2.gif"/></inline-formula>, we let <inline-formula><graphic file="1029-242X-2006-92795-i3.gif"/></inline-formula> be the space of all analytic functions <inline-formula><graphic file="1029-242X-2006-92795-i4.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-92795-i5.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2006-92795-i6.gif"/></inline-formula> belongs to the weighted Bergman space <inline-formula><graphic file="1029-242X-2006-92795-i7.gif"/></inline-formula>. We obtain a number of sharp results concerning the existence of tangential limits for functions in the spaces <inline-formula><graphic file="1029-242X-2006-92795-i8.gif"/></inline-formula>. We also study the size of the exceptional set <inline-formula><graphic file="1029-242X-2006-92795-i9.gif"/></inline-formula>, where <inline-formula><graphic file="1029-242X-2006-92795-i10.gif"/></inline-formula> denotes the radial variation of <inline-formula><graphic file="1029-242X-2006-92795-i11.gif"/></inline-formula> along the radius <inline-formula><graphic file="1029-242X-2006-92795-i12.gif"/></inline-formula>, for functions <inline-formula><graphic file="1029-242X-2006-92795-i13.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/2006/927957 |
| spellingShingle | Peláez José Ángel Girela Daniel Boundary behaviour of analytic functions in spaces of Dirichlet type Journal of Inequalities and Applications |
| title | Boundary behaviour of analytic functions in spaces of Dirichlet type |
| title_full | Boundary behaviour of analytic functions in spaces of Dirichlet type |
| title_fullStr | Boundary behaviour of analytic functions in spaces of Dirichlet type |
| title_full_unstemmed | Boundary behaviour of analytic functions in spaces of Dirichlet type |
| title_short | Boundary behaviour of analytic functions in spaces of Dirichlet type |
| title_sort | boundary behaviour of analytic functions in spaces of dirichlet type |
| url | http://www.journalofinequalitiesandapplications.com/content/2006/927957 |
| work_keys_str_mv | AT pel225ezjos233193ngel boundarybehaviourofanalyticfunctionsinspacesofdirichlettype AT gireladaniel boundarybehaviourofanalyticfunctionsinspacesofdirichlettype |