Trace principle for Riesz potentials on Herz-type spaces and applications

Abstract

Abstract We establish trace inequalities for Riesz potentials on Herz-type spaces and examine the optimality of conditions imposed on specific parameters. We also present some applications in the form of Sobolev-type inequalities, including the Gagliardo–Nirenberg–Sobolev inequality and the fractional integration theorem in the Herz space setting. In addition, we obtain a Sobolev embedding theorem for Herz-type Sobolev spaces.

Keywords

• Riesz potential
• Adams’ trace inequality
• Herz spaces
• Sobolev inequalities