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Characterization for Beurling-Björck space and Schwartz space


Authors: Soon-Yeong Chung, Dohan Kim and Sungjin Lee
Journal: Proc. Amer. Math. Soc. 125 (1997), 3229-3234
MSC (1991): Primary 46F05, 46F12, 42B10
DOI: https://doi.org/10.1090/S0002-9939-97-04221-4
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 $\mathcal {S}$. 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.


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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

Keywords: Fourier transform, Schwartz space, Beurling–Björck 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
Article copyright: © Copyright 1997 American Mathematical Society