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Optimal extension of the Fourier transform and convolution operator on compact groups
Indagationes Mathematicae ( IF 0.6 ) Pub Date : 2020-03-01 , DOI: 10.1016/j.indag.2020.01.003
Manoj Kumar , N. Shravan Kumar

Let $G$ be a compact group (not necessarily abelian) and let $\Phi$ be a Young function satisfying the $\Delta_2$-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces $L^\Phi(G).$

中文翻译:

紧群上傅里叶变换和卷积算子的优化扩展

让 $G$ 是一个紧群(不一定是阿贝尔群),让 $\Phi$ 是一个满足 $\Delta_2$ 条件的 Young 函数。我们确定了在 Orlicz 空间 $L^\Phi(G).$ 上定义的傅立叶变换和卷积算子的最佳域和相关的扩展算子。
更新日期:2020-03-01
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