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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
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
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

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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