Hardy inequalities for fractional integrals on general domains

Journal of Functional Analysis

Volumn 259, Issue 6, 2010, Pages 1369-1379

  Loss, Michael ^a   Sloane, Craig ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Best constant; Fractional Hardy inequality; Fractional Laplacian

Indexed keywords

EID: 77954142411     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2010.05.001     Document Type: Article

References (14)

1. Barbatis G., Filippas S., Tertikas A. A unified approach to improved Lp Hardy inequalities with best constants. Trans. Amer. Math. Soc. 2004, 356(6):2169-2196.
2. Bogdan K., Dyda B. The best constant in a fractional Hardy inequality arxiv:/0807.1825.
3. Bogdan K., Burdzy K., Chen Z.-Q. Censored stable processes. Probab. Theory Related Fields 2003, 127:89-152.
4. Carlen E.A., Loss M. On the minimization of symmetric functionals. Rev. Math. Phys. 1994, 1011-1032.
5. Chen Z.-Q., Song R. Hardy inequality for censored stable processes. Tohoku Math. J. 2003, 55:439-450.
6. Davies E.B. Some norm bounds and quadratic form inequalities for Schrödinger operators, II. J. Operator Theory 1984, 12:177-196.
7. Davies E.B. Heat Kernels and Spectral Theory. Cambridge Tracts in Math. 1989, Cambridge University Press.
8. Davies E.B. A review of Hardy inequalities. Oper. Theory Adv. Appl. 1999, vol. 110:55-67. Birkhäuser, Basel.
9. Dyda B. A fractional order Hardy inequality. Illinois J. Math. 2004, 48:575-588.
10. Frank R.L., Seiringer R. Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 2008, 255:3407-3430.
11. Frank R., Seiringer R. Sharp fractional Hardy inequalities in half-spaces arxiv:/0906.1561.
12. Heinig H.P., Kufner A., Persson L.-E. On some fractional order Hardy in equalities. J. Inequal. Appl. 1997, 1:25-46.
13. Marcus M., Mizel V.J., Pinchover Y. On the best constant for Hardy's inequality in Rn. Trans. Amer. Math. Soc. 1998, 350:3237-3255.
14. Matskewich T., Sobolevskii P.E. The best possible constant in generalized Hardy's inequality for convex domain in Rn. Nonlinear Anal. 1997, 28:1601-1610.