Duals and envelopes of some Hardy-Lorentz spaces

Author:
Marc Lengfield

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1401-1409

MSC (2000):
Primary 32A35

DOI:
https://doi.org/10.1090/S0002-9939-04-07656-7

Published electronically:
October 18, 2004

MathSciNet review:
2111965

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Abstract | References | Similar Articles | Additional Information

Abstract: For we describe the dual spaces and Banach envelopes of the spaces for finite values of and for , the closure of the polynomials in . In addition, we determine the -Banach envelopes for the spaces in the cases and .

**1.**A.B. Aleksandrov,*Essays on nonlocally convex Hardy classes*, Complex analysis and spectral theory, ed. V.P. Havin and N.K. Nikolskii, Springer Lecture Notes in Math.**864**(1981), 1-89. MR**0643380 (84h:46066)****2.**R.R. Coifman and R. Rochberg,*Representation theorems for holomorphic and harmonic functions in*, Astérique**77**(1980), 110-150. MR**0604369 (82j:32015)****3.**Peter L. Duren,*Theory of 𝐻^{𝑝} spaces*, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR**0268655****4.**P. L. Duren, B. W. Romberg, and A. L. Shields,*Linear functionals on 𝐻^{𝑝} spaces with 0<𝑝<1*, J. Reine Angew. Math.**238**(1969), 32–60. MR**0259579****5.**Joaquín M. Ortega and Joan Fàbrega,*Mixed-norm spaces and interpolation*, Studia Math.**109**(1994), no. 3, 233–254. MR**1274011****6.**G.H. Hardy and J.E. Littlewood,*Some properties of fractional integrals, II*, Math. Z.**34**(1932), 403-439.**7.**P.W. Jones,*estimates for the**problem in the half-plane*, Acta Math.**150**(1983), 137-152. MR**0697611 (84g:35135)****8.**N.J. Kalton,*Linear operators on**spaces for*, Trans. Amer. Math. Soc.**259**(1980), 319-355. MR**0567084 (81d:47022)****9.**J.H. Shi,*On the rate of growth of the means**of holomorphic and pluriharmonic functions on bounded symmetric domains of*, J. Math. Anal. Appl.**26**(1987), 161-175. MR**0900536 (89d:32011)**

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Additional Information

**Marc Lengfield**

Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510

Address at time of publication:
Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101

Email:
mlang@math.fsu.edu, marc.lengfield@wku.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07656-7

Received by editor(s):
April 1, 2003

Received by editor(s) in revised form:
January 7, 2004

Published electronically:
October 18, 2004

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.