We establish trace inequalities for Riesz potentials on Herz-type spaces and discuss 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.
No takes yet. Share an insight, caveat, or question.
Bhat et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: