© Hindawi Publishing Corp. FOURIER TRANSFORMS OF LIPSCHITZ FUNCTIONS ON CERTAIN LIE GROUPS

Abstract. We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the special linear group of real matrices of order two. 2000 Mathematics Subject Classification. 42A38, 44A15, 42C99, 44A05. 1. Introduction. The order of magnitude of the Fourier transforms (coefficients) of Lipschitz functions on various domains is an active field of investigation. For example in [9, 11] this problem was studied for Lipschitz functions on the groups SU(2) and SU(1,1). In the present work we take the same problem for Lipschitz functions but defined on SL(2,R), the special linear group of real matrices of order two. This note i