Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Duals and envelopes of some Hardy-Lorentz spaces

Author: Marc Lengfield
Journal: Proc. Amer. Math. Soc. 133 (2005), 1401-1409
MSC (2000): Primary 32A35
Published electronically: October 18, 2004
MathSciNet review: 2111965
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For $0<p<1$ we describe the dual spaces and Banach envelopes of the spaces $H^{p,q}$ for finite values of $q$ and for $H_{0}^{p,\infty }$, the closure of the polynomials in $H^{p,\infty }$. In addition, we determine the $s$-Banach envelopes for the spaces $H^{p,q}$ in the cases $0<q<p<s\leq 1$ and $0<q<p\leq s\leq 1$.

References [Enhancements On Off] (What's this?)

  • 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 $L^{p}$, 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, $L^{\infty }$ estimates for the $\bar {\partial }$ problem in the half-plane, Acta Math. 150 (1983), 137-152. MR 0697611 (84g:35135)
  • 8. N.J. Kalton, Linear operators on $L^{p}$ spaces for $0<p<1$, Trans. Amer. Math. Soc. 259 (1980), 319-355. MR 0567084 (81d:47022)
  • 9. J.H. Shi, On the rate of growth of the means $M_{p}$ of holomorphic and pluriharmonic functions on bounded symmetric domains of $\mathbb{C} ^{n}$, J. Math. Anal. Appl. 26 (1987), 161-175. MR 0900536 (89d:32011)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A35

Retrieve articles in all journals with MSC (2000): 32A35

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

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.

American Mathematical Society