论文标题
局部紧凑型组的可变lebesgue代数
Variable Lebesgue algebra on a Locally Compact group
论文作者
论文摘要
对于具有左HAAR度量的本地紧凑型组$ h $，我们研究了lebesgue代数$ \ Mathcal {l}^{p（\ cdot）}（h）$，相对于卷积。我们表明，如果$ \ Mathcal {l}^{p（\ cdot）}（h）$具有有限的指数，则它包含左近似身份。我们还证明了具有$ \ Mathcal {l}^{p（\ cdot）}（h）$具有身份的必要条件。我们观察到，$ \ Mathcal {l}^{p（\ cdot）}（h）$的封闭线性子空间是左侧的理想时，并且仅当它被左图不变时。
For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has bounded exponent, then it contains a left approximate identity. We also prove a necessary and sufficient condition for $\mathcal{L}^{p(\cdot)}(H)$ to have an identity. We observe that a closed linear subspace of $\mathcal{L}^{p(\cdot)}(H)$ is a left ideal if and only if it is left translation invariant.
