Multilinear Riesz Potential on Morrey-Herz Spaces with Non-Doubling Measures

Abstract

The authors consider the multilinear Riesz potential operator defined by ℐα,m(f⃗)(x)=∫(ℝd)m(f1(y1)f2(y2)⋯fm(ym)/|(x-y1,…,x-ym)|mn-α)dμ(y1)⋯dμ(ym), where f⃗ denotes the m-tuple (f1,f2,…,fm), m,n the nonnegative integers with n≥2, m≥1, 0<α<mn, and μ is a nonnegative n-dimensional Borel measure. In this paper, the boundedness for the operator ℐα,m on the product of homogeneous Morrey-Herz spaces in nonhomogeneous setting is found.