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Envelopes, Duality, and Multipliers for Certain Non-Locally Convex Hardy-Lorentz Spaces
| Title: | Envelopes, Duality, and Multipliers for Certain Non-Locally Convex Hardy-Lorentz Spaces. |
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| Name(s): |
Lengfield, Marc, author Oberlin, Daniel M., professor directing dissertation McKeague, Ian, outside committee member Bellenot, Steven, committee member Nolder, Craig, committee member Department of Mathematics, degree granting department Florida State University, degree granting institution |
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| Type of Resource: | text | |
| Genre: | Text | |
| Issuance: | monographic | |
| Date Issued: | 2004 | |
| Publisher: | Florida State University | |
| Place of Publication: | Tallahassee, Florida | |
| Physical Form: |
computer online resource |
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| Extent: | 1 online resource | |
| Language(s): | English | |
| Abstract/Description: | This dissertation is a study of the Hardy-Lorentz spaces Hp,q for indices in the range 0 < p < 1, 0 < q ≤ ∞. More precisely, for p as indicated, we describe the dual spaces and Banach envelopes of the spaces Hp,q for finite values of q and do the same for H0p,∞, the closure of the polynomials in Hp,∞. In addition, we determine the s-Banach envelopes for the spaces Hp,q in the cases 0 < q < p < s ≤ 1 and 0 < p < q ≤ s ≤ 1. As an application of our results we determine the multiplier spaces (Hp,q, ℓs) for 0 < p < 1, 0 < q, s ≤ ∞. | |
| Identifier: | FSU_migr_etd-3131 (IID) | |
| Submitted Note: | A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. | |
| Degree Awarded: | Spring Semester, 2004. | |
| Date of Defense: | January 5, 2004. | |
| Keywords: | Hardy Spaces, Lorentz Spaces, Hardy-Lorentz Spaces, Multipliers, Coefficient Multipliers, Dual Space, Duality, Envelopes, Analytic Function, Duren-Romberg-Shields Theorem | |
| Bibliography Note: | Includes bibliographical references. | |
| Advisory Committee: | Daniel M. Oberlin, Professor Directing Dissertation; Ian McKeague, Outside Committee Member; Steven Bellenot, Committee Member; Craig Nolder, Committee Member. | |
| Subject(s): | Mathematics | |
| Persistent Link to This Record: | http://purl.flvc.org/fsu/fd/FSU_migr_etd-3131 | |
| Owner Institution: | FSU |
Lengfield, M. (2004). Envelopes, Duality, and Multipliers for Certain Non-Locally Convex Hardy-Lorentz Spaces. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-3131
