Characterization for Beurling-Björck space and Schwartz space |
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| Authors: | Soon-Yeong Chung Dohan Kim Sungjin Lee |
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| Affiliation: | Department of Mathematics, Sogang University, Seoul 121--742, Korea ; Department of Mathematics, Seoul National University, Seoul 151--742, Korea ; Department of Mathematics, Daejin University, Pochun 487--800, Korea |
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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. |
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| Keywords: | Fourier transform, Schwartz space, Beurling--Bj" {o}rck space, tempered, ultradistributions |
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