IJPAM: Volume 36, No. 2 (2007)

ON THE YOUNG THEOREM FOR AMALGAMS
AND BESOV SPACES

Yoshihiro Sawano$^1$, Tsuyoshi Yoneda$^2$
$^{1,2}$Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, JAPAN
$^1$e-mail: yosihiro@ms.u-tokyo.ac.jp
$^2$e-mail: yoneda@ms.u-tokyo.ac.jp


Abstract.In this paper, we obtain a refinement of the Young Theorem. The Young Theorem tells us that the Fourier transform $\cF$ sends the $L^p$ functions to the $L^{p'}$ functions, if $1 \le p \le 2$. This theorem has a refinement. For example, $\cF:L^1 \to B_{\infty 1}^0$, where $B_{pq}^s$ is the Besov space. In this present paper we shall consider the more refined version of this theorem by using the amalgams and the Besov spaces.

Received: August 18, 2006

AMS Subject Classification: 42B10, 42B35

Key Words and Phrases: Besov space, amalgam space, Fourier transform

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 2