A fractional Hardy-Sobolev-Maz'ya inequality on the upper halfspace

Proceedings of the American Mathematical Society

Volumn 139, Issue 11, 2011, Pages 4003-4016

  Sloane, Craig A ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960751605     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2011-10818-9     Document Type: Article

References (14)

1. R. Adams, J. Fournier, Sobolev Spaces. Second edition. Elsevier/Acad. Press, Amsterdam, 2003. MR2424078 (2009e:46025)
2. K. Bogdan, K. Burdzy, and Z.Q. Chen, Censored Stable Processes, Probab. Theory Related Fields 127, 89-152 (2003). MR2006232 (2004g:60068)
3. K. Bogdan, B. Dyda, The Best Constant in a Fractional Hardy Inequality, arXiv:0807.1825v1 [math.AP] (2008).
4. R. Benguria, R. Frank, M. Loss, The Sharp Constant in the Hardy-Sobolev-Maz'ya Inequality in the Three Dimensional Upper Half-Space, Math. Res. Lett. 15, no. 4, 613-622 (2008). MR2424899 (2009j:46074)
5. E. Carlen, M. Loss, Extremals of Functionals with Competing Symmetries, J. Funct. Anal. 88 no. 2, 437-456 (1990). MR1038450 (91f:42021)
6. E. Carlen, M. Loss, On the Minimization of Symmetric Functionals. Special Issue Dedicated to Elliott H. Lieb. Rev. Math. Phys. 6, no. 5A, 1011-1032 (1994). MR1301364 (96k:58068)
7. B. Dyda, A Fractional Order Hardy Inequality, Ill. J. Math. 48, no. 2, 575-588 (2004). MR2085428 (2005f:26054)
8. R. Frank, R. Seiringer, Non-linear Ground State Representations and Sharp Hardy Inequalities, J. Funct. Anal. 255, 3407-3430 (2008). MR2469027 (2009k:46058)
9. R. Frank, R. Seiringer, Sharp Fractional Hardy Inequalities in Half-Spaces. In: Around the research of Vladimir Maz'ya, A. Laptev (ed.), 161-167, International Mathematical Series, 11, Springer, New York, 2010. MR2723817
10. S. Filippas, A. Tertikas, J. Tidblom, On the Structure of Hardy-Sobolev-Maz'ya Inequalities (English summary), J. Eur. Math. Soc. 11, no. 6, 1165-1185 (2009). MR2557132
11. E. Lieb, M. Loss. Analysis. Graduate Studies in Mathematics, vol. 14, Amer. Math. Society, Providence, RI, 2nd edition, 2001. MR1817225 (2001i:00001)
12. M. Loss, C. Sloane, Hardy Inequalities for Fractional Integrals on General Domains, J. Funct. Anal. 259, no. 6, 1369-1379 (2010). MR2659764
13. V. Mazya. Sobolev Spaces. Translated from the Russian by T. O. Shaposhnikova. Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1985. MR817985 (87g:46056)
14. A. Tertikas, K. Tintarev, On Existence of Minimizers for the Hardy-Sobolev-Maz'ya Inequality, Ann. Mat. Pura Appl. 186, 645-662 (2007). MR2317783 (2008j:35069)