论文标题
titchmarsh定理在damek-ricci空间上通过高阶连续性
Titchmarsh theorems on Damek-Ricci spaces via moduli of continuity of higher order
论文作者
论文摘要
Titchmarsh的经典定理将函数的$ l^2 $ -Lipschitz函数和功能的傅立叶变换的衰减相关联。在本说明中，我们通过更高订单的连续性证明了damek-ricci空间（也称为谐波$ na $组）的Titchmarsh定理。我们还证明了另一个titchmarsh定理的类似物，该定理为HölderLipschitz空间中的功能提供了傅立叶变换的集成性属性。
A classical theorem of Titchmarsh relates the $L^2$-Lipschitz functions and decay of the Fourier transform of the functions. In this note, we prove the Titchmarsh theorem for Damek-Ricci space (also known as harmonic $NA$ groups) via moduli of continuity of higher orders. We also prove an analogue of another Titchmarsh theorem which provides integrability properties of the Fourier transform for functions in the Hölder Lipschitz spaces.
