[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2012.25.3.527

FRACTIONAL RELLICH-KONDRACHOV COMPACTNESS THEOREM

Park, Young Ja (Department of Mathematics Hoseo University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.25, no.3, 2012 , pp. 527-529 More about this Journal

Abstract

It is proved that the fractional Sobolev spaces $W^s_p(\mathbb{R}^n)$ 0 < $s$ < $n$ , are compactly embedded into Lebesgue spaces $L^q(\Omega)$ for some bounded set $\Omega$ .

Keywords

compactness theorem; fractional Sobolev inequality; fractional Laplacian;

Citations & Related Records

Reference

1	W. Beckner, Inequalities in Fourier analysis, Ann. Math. 102 (1975), 159-182. DOI
2	W. Beckner, Geometric inequalities in Fourier analysis, Essays on Fourier Analysis in honor of Elias M. Stein, Princeton University Press, Princeton, NJ, 36-68, 1995.
3	W. Beckner, Multilinear embedding estiamtes for the fractional Laplacian, arXiv:1004. 2259v2.[math.AP] 22 Apr 2010.
4	L. C. Evans, Partial differentail equaltions, Volume 19 of Graduate Studies in Mathematics, AMS, 1998.
5	E. H. Lieb and M. Loss, Analysis, Volume 14 of Graduate Studies in Mathe- matics, AMS, 1997.
6	Y. J. Park, Fractional Gagliardo-Nirenberg inequality, Journal of the Chungcheong Mathematical Society 24 (2011), 583-586.
7	R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, volume 49 of Math. Surveys and Monographs, AMS, 1997.