Inequalities in homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces

This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by $ \dot{F}^s_{p,q}(\mathbb R^n) \dot{B}^s_{p,q}(\mathbb respectively, in terms maximal functions the mean values iterated difference. It also furnishes reader with inequalities difference along coordinate axes. The corresponding axes are considered. techniques used this Fourier analytic nature Hardy-Littlewood Peetre-Fefferman-Stein functions.