Fourier transforms of Lipschitz functions on certain Lie groups (Q1348724)

The order of magnitude of Fourier transforms is studied. This problem was solved earlier by the author for Lipschitz functions on the groups SU(2) and SU(1,1). In the present paper the same problem is discussed for Lipschitz functions on the special linear group of real matrices of order two, i.e. \(\text{SL} (2,\mathbb{R})\). The main conclusions obtained in \(L^2\) are extended to functions in \(L^p\), \(1<p\leq 2\). The last section is devoted to possible further extensions.