INEQUALITIES IN HOMOGENEOUS TRIEBEL-LIZORKIN AND BESOV-LIPSCHITZ SPACES

This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by Fsp,q(Rn) and Bsp,q(Rn) respectively, in terms of maximal functions of the mean values of iterated difference. It also furnishes the reader with inequalities in Fsp,q(Rn) in terms of iterated difference and in terms of iterated difference along coordinate axes. The corresponding inequalities in Bsp,q(Rn) in terms of iterated difference and in terms of iterated difference along coordinate axes are also considered. The techniques used in this paper are of Fourier analytic nature and the HardyLittlewood and Peetre-Fefferman-Stein maximal functions.