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| SEGAL ALGEBRA $\[{A_{1,p}}(G)\]$ AND ITS MULTIPLIERS |
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Citation： |
Ouyang Guangzhong.SEGAL ALGEBRA $\[{A_{1,p}}(G)\]$ AND ITS MULTIPLIERS[J].Chinese Annals of Mathematics B,1986,7(3):365~372 |
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Net amount： 741 |
Authors： |
Ouyang Guangzhong; |
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| Abstract： |
Let G be a locally compactb abelian group and $\[{A_p}(G)\]$ the p-Fourier algeba of Herz.
This pepar studies the space $\[{A_{1,p}}(G) = {L_1}(G) \cap {A_p}(G)\]$ with convolution product. It is
proved that $\[{A_{1,p}}(G)\]$ is a character Segal algebra. Moreover, for the multipliers of $\[{A_{1,p}}(G)\]$ the author proves that $\[M({A_{1,p}}(G),{L_1}(G)) = M(G)\]$ and $\[M({A_{1,p}}(G),{A_{1,p}}(G)) = M(G)\]$
provided G is noncompact. If G is discrete, then $\[M({A_{1,p}}(G),{L_1}(G)) = {A_{1,p}}(G)\$ and
$\[M({A_{1,p}}(G),{A_{1,p}}(G)) = {A_{1,p}}(G)\]$ |
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