INTEGRAL-REPRESENTATIONS, DIFFERENTIABILITY PROPERTIES AND LIMITS AT INFINITY FOR BEPPO-LEVI FUNCTIONS

The first aim in the present paper is to give an integral representati on for Beppo Levi functions on R-n. Our integral representation is an extension of Sobolev's integral representation given for infinitely di fferentiable functions with compact support. As applications, continui ty and differentiability properties of Beppo Levi functions are studie d. Our second aim in this paper is to study the existence of limits at infinity for Beppo Levi functions. We also consider the existence of fine-type limits at infinity with respect to Bessel capacities, which yields the radial limit result at infinity.