ABSTRACT
This chapter aims to set up some notation and considers some fundamental properties. It also considers the convolution estimates, where the moment conditions come into play. The chapter compares the norm of the derivatives and the Lq -norm. It then consider the approximation of functions by polynomials and investigates the dimension of the space. The moment condition defined is an important condition which will leads to a nontrivial estimate; the triangle inequality is beyond our reach. A spherical harmonic is a function obtained by restricting harmonic functions to the unit sphere. The chapter summarizes some useful estimates for spherical harmonics. It explores some equalities for homogeneous harmonic functions.
