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Conditions on the Logarithmic Derivative of a Function Implying Boundedness
| Content Provider | Scilit |
|---|---|
| Author | F. Rønning Gregor, T. H. Mac |
| Copyright Year | 1995 |
| Description | In this paper we investigate functions analytic and nonvanishing in the unit disk, with the property that the logarithmic derivative is contained in some domain $\Omega$. We obtain conditions on $\Omega$ which imply that the functions are bounded and that their first derivatives belong to ${H^p}$ for some $p \geqslant 1$. For certain domains $\Omega$ the sufficient conditions that we give are also, in some sense, necessary. Examples of domains to which the results apply are given. |
| Related Links | https://www.ams.org/tran/1995-347-06/S0002-9947-1995-1277126-9/S0002-9947-1995-1277126-9.pdf |
| Ending Page | 2254 |
| Page Count | 10 |
| Starting Page | 2245 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/2154937 |
| Journal | Transactions of the American Mathematical Society |
| Issue Number | 6 |
| Volume Number | 347 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1995-06-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Functions Logarithmic Derivative Give Disk Geqslant Belong Sufficient Nonvanishing Implying Boundedness |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
