Multidimensional fractional integrals and distributions

Abstract

New spaces of generalized functions on Rⁿ are introduced. These spaces generalize corresponding spaces on R₊ studied previously by the first author. Basic properties are obtained in preparation for a study of fractional integrals, including Riesz potentials, in a companion paper.

Keywords:

• test function
• generalized function
• fractional integral

MSC(1991):

• 26A33
• 46F05