2024/03/09 by M. Ashraf Bhat, Bhat, M. Ashraf, G. Sankara Raju Kosuru +1
Mathematics · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2403.05929
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.