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| ON THE $\[{L^p}\]$-BOUNDEDNESS OF SEVERAL CLASSES OF PSEUDO-DIF FERENTIAL OPERATORS |
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Citation： |
Wang Rouhuai,Li Chengzhang.ON THE $\[{L^p}\]$-BOUNDEDNESS OF SEVERAL CLASSES OF PSEUDO-DIF FERENTIAL OPERATORS[J].Chinese Annals of Mathematics B,1984,5(2):193~214 |
| Page view： 697
Net amount： 801 |
Authors： |
Wang Rouhuai; Li Chengzhang |
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| Abstract： |
To indicate precisely the requirements for smoothness of symbols, generalizations of Hormander's classes of symbols, $\[S_{p,k,\delta ,\nu }^m\]$ and $\[S_{p,k,\delta ,\nu ,\varepsilon ,x}^m\]$ are introduced. The main results are as follows: (1) An optimal $\[{L^p}\]$-boundedness result is obtained for the pseudo-differential
operators with double symbols (amplitude) $\[a(x,\xi ,y)\]$; (2) By means of the interpolation theorem 4 due to Fefferman and Stein, new $\[{L^p}\]$-boundedness results are established. These results are not only sharp with respect to upper index, but also sharp $\[(p \ge 2)\]$ or almost sharp $\[(1 < p < 2)\]$ with respect to lower indices. |
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