Type of Document	Dissertation
Author	Lengfield, Marc Roy
Author's Email Address	mlang@math.fsu.edu
URN	etd-04062004-110656
Title	Envelopes, Duality, And Multipliers For Certain Non-Locally Convex Hardy-Lorentz Spaces
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Daniel Oberlin Committee Chair Craig Nolder Committee Member ian McKeague Committee Member Steven Bellenot Committee Member
Keywords	Hardy Spaces Lorentz Spaces Hardy-Lorentz Spaces Multipliers Coefficient Multipliers Dual Space Duality Envelopes Analytic Function Duren-Romberg-Shields Theorem
Date of Defense	2004-01-05
Availability	unrestricted
Abstract This dissertation is a study of the Hardy-Lorentz spaces Hsp{p,q} for indices in the range 0 < p < 1, 0 < q leq infty. More precisely, for p as indicated, we describe the dual spaces and Banach envelopes of the spaces Hsp{p,q} for finite values of q and do the same for Hsp{p,infty}sb{0}, the closure of the polynomials in Hsp{p,infty}. In addition, we determine the $s$-Banach envelopes for the spaces Hsp{p,q} in the cases 0 < q < p < s leq 1 and 0 < p < q leq s leq 1. As an application of our results we determine the multiplier spaces (Hsp{p,q}, ellsp{s}) for 0 < p < 1, 0 < q,s leq infty.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    lengfield.pdf 1.42 Mb 00:06:33 00:03:22 00:02:57 00:01:28 00:00:07