Sharp singular Adams inequalities in high order Sobolev spaces

@article{Lam2011SharpSA,
  title={Sharp singular Adams inequalities in high order Sobolev spaces},
  author={Nguyen Huong Lam and Guozhen Lu},
  journal={arXiv: Analysis of PDEs},
  year={2011}
}
  • N. Lam, G. Lu
  • Published 29 December 2011
  • Mathematics
  • arXiv: Analysis of PDEs
In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in $\mathbb{R}^{n}$. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend the singular Moser-Trudinger inequalities of first order in \cite{Ad2, R, LR, AdY} to… 
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