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Characterization for Beurling-Björck space and Schwartz space
Author(s):
Soon-Yeong
Chung;
Dohan
Kim;
Sungjin
Lee
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3229-3234.
MSC (1991):
Primary 46F05, 46F12, 42B10
MathSciNet review:
1443817
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Abstract:
We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space  . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.
References:
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Additional Information:
Soon-Yeong
Chung
Affiliation:
Department of Mathematics, Sogang University, Seoul 121--742, Korea
Email:
sychung@ccs.sogang.ac.kr
Dohan
Kim
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151--742, Korea
Email:
dhkim@math.snu.ac.kr
Sungjin
Lee
Affiliation:
Department of Mathematics, Daejin University, Pochun 487--800, Korea
Email:
hyper@math.snu.ac.kr
DOI:
10.1090/S0002-9939-97-04221-4
PII:
S 0002-9939(97)04221-4
Keywords:
Fourier transform,
Schwartz space,
Beurling--Bj\"{o}rck space,
tempered,
ultradistributions
Received by editor(s):
December 11, 1995
Additional Notes:
This work was partially supported by GARC--KOSEF and BSRI
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1997,
American Mathematical Society
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