Lipschitz conditions in Damek-Ricci spaces
The paper gives a complete characterization of the (Dini-) Lipschitz conditions for $L^2$ space on Damek-Ricci spaces by estimating the norm of the Fourier-Helgason transform. A necessary characterization of the (Dini-) Lipschitz conditions for the $L^p$ space when $1< p< 2$ is nicely presented. Furthermore, the norm of the Fourier-Helgason transform is also estimated for functions in the (Dini-) Lipschitz class. The results greatly improve the ones obtained by \textit{E. C. Titchmarsh} [Introduction to the theory of Fourier integrals. Oxford: Clarendon Press (1937; Zbl 0017.40404)].
scientific article; zbMATH DE number 7390651
scientific article