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The Banach envelope of Paley-Wiener type spaces
Author(s):
Mark
Hoffmann
Journal:
Proc. Amer. Math. Soc.
131
(2003),
543-548.
MSC (2000):
Primary 46A16, 30D15
Posted:
June 5, 2002
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Abstract:
We give an explicit computation of the Banach envelope for the Paley-Wiener type spaces . This answers a question by Joel Shapiro.
References:
- 1.
- R. P. Boas, Entire functions, Academic Press, New York, 1954. MR 16:914f
- 2.
- R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in
, Astérisque 77 (1980) 11-66. MR 82j:32015 - 3.
- R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977) 569-645. MR 56:6264
- 4.
- P. L. Duren, Theory of
spaces, Academic Press, New York/London, 1970. MR 42:3552 - 5.
- P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on
spaces when , J. Reine Angew. Math. 238 (1969) 32-60. MR 41:4217 - 6.
- C. Eoff, The discrete nature of the Paley-Wiener spaces, Proc. Amer. Math. Soc. 123 (1995) 505-512. MR 95c:42011
- 7.
- J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985. MR 87d:42023
- 8.
- N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, London Mathematical Society, LNS No. 89, 1984. MR 87c:46002
- 9.
- N. J. Kalton and D. A. Trautman, Remarks on subspaces of
when , Michigan Math. J. 29 (1982) 163-171. MR 83i:46030 - 10.
- P. Koosis, Introduction to
spaces, Cambridge Univ. Press, 2nd ed. 1998. MR 2000b:30052 - 11.
- O. Mendez and M. Mitrea, The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations, J. Fourier Anal. Appl. 6 (2000) 503-533. MR 2001k:46056
- 12.
- M. Mitrea, Banach envelopes of holomorphic Hardy spaces, preprint, 2000.
- 13.
- A. Pe
czynski, Projections in certain Banach spaces, Studia Math. 19 (1960) 209-228. MR 23:A3441 - 14.
- M. Plancherel and G. Pólya, Fonctions entières et intègrales de Fourier multiples, Comment. Math. Helv. 10 (1937) 110-163.
- 15.
- F. Ricci and M. Taibleson, Boundary Values of Harmonic Functions in Mixed Norm Spaces and Their Atomic Structure, Ann. Scuola Norm. Sup. Pisa 10 (1983) 1-54. MR 85m:30025
- 16.
- H. Triebel, Theory of function spaces II, Birkhäuser, Berlin, 1992. MR 93f:46029
- 17.
- J. H. Shapiro, Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces, Duke Math. J. 43 (1976) 187-202. MR 58:17806
- 18.
- E. M. Stein, Harmonic analysis: Real-Variable Methods, Orthogonality, and Oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 95c:42002
- 19.
- W. J. Stiles, Some properties of
, , Studia Math. 42 (1972) 109-119. MR 46:7840 - 20.
- P. Wojtaszczyk,
-spaces, , and spline systems , Studia Math. 77 (1984) 289-320. MR 85f:46053
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Additional Information:
Mark
Hoffmann
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email:
mathgr26@math.missouri.edu
DOI:
10.1090/S0002-9939-02-06581-4
PII:
S 0002-9939(02)06581-4
Keywords:
Paley-Wiener spaces,
Banach envelopes
Received by editor(s):
June 6, 2001
Received by editor(s) in revised form:
September 25, 2001
Posted:
June 5, 2002
Additional Notes:
The author was partially supported by NSF grant DMS-9870027
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2002,
American Mathematical Society
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