Multipliers and extremal problems in Bergman spaces.
dc.contributor.author | Vukotic, Dragan | en_US |
dc.contributor.advisor | Duren, Peter L. | en_US |
dc.date.accessioned | 2014-02-24T16:16:35Z | |
dc.date.available | 2014-02-24T16:16:35Z | |
dc.date.issued | 1993 | en_US |
dc.identifier.other | (UMI)AAI9332180 | en_US |
dc.identifier.uri | http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:9332180 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/103680 | |
dc.description.abstract | In this thesis we consider two topics in the theory of Bergman spaces $A\sp{p}.$. We study the existence and uniqueness of functions for which the norm of a bounded linear functional on $A\sp{p}$ is attained. In the general case, by means of techniques from approximation theory, we prove a theorem which characterizes the extremal function in terms of an integral condition and relates it to a certain Sobolev space. In some particular cases, we are able to determine the extremal function explicitly by making use of this theorem or of involutive subjective isometries of $A\sp{p}.$. We also study the coefficient multipliers from $A\sp{p}$ into $A\sp{q},$ and obtain some new sufficient and/or necessary conditions. In particular, an analogue of a theorem of Duren about multipliers of $H\sp{p}$ spaces is obtained, as well as the analogue of a known theorem of Hardy-Littlewood-Duren-Shields on Hardy spaces, thus completely characterizing the multipliers from $A\sp1$ into $A\sp2.$ Further results are included. | en_US |
dc.format.extent | 61 p. | en_US |
dc.subject | Mathematics | en_US |
dc.title | Multipliers and extremal problems in Bergman spaces. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/103680/1/9332180.pdf | |
dc.description.filedescription | Description of 9332180.pdf : Restricted to UM users only. | en_US |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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