Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | On Lipschitz and α-Bloch spaces on the unit polydisc | Journal: | Studia Scientiarum Mathematicarum Hungarica | Volume: | 45 | Issue: | 3 | First page: | 361 | Last page: | 378 | Issue Date: | 1-Sep-2008 | Rank: | M23 | ISSN: | 0081-6906 | DOI: | 10.1556/SScMath.2008.1056 | Abstract: | In this paper we show that if (0, 1), the holomorphic Lipschitz space Lalpha;( ) on the unit polydisc is equivalent to the 1 - -Bloch space , as well as to the space consisting of all holomorphic functions f on , continuous on the closure of and satisfying the following condition where e i is an abbreviation for ( ). Moreover, we show that the corresponding norms , and , on these spaces are comparable, that is, there are positive constants C 1, C 2 and C 3 depending only on and n such that for every f holomorphic on . |
Keywords: | Analytic function | Bloch space | Lipschitz type space | Polydisc | Publisher: | AKJournals |
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