Fractional Hardy-Sobolev-Maz'ya inequality for domains

Studia Mathematica

Volumn 208, Issue 2, 2012, Pages 151-166

  Dyda, Bartlomiej ^a,b   Frank, Rupert L ^c  

^a BIELEFELD UNIVERSITY   (Germany)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

Fractional Hardy inequality; Fractional Hardy Sobolev Maz'ya inequality

Indexed keywords

EID: 84861447031     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm208-2-3     Document Type: Article

References (15)

1. G. Barbatis, S. Filippas, and A. Tertikas, A unified approach to improved Lp Hardy inequalities with best constants, Trans. Amer. Math. Soc. 356 (2004), 2169-2196. (Pubitemid 38671218)
2. R. D. Benguria, R. L. Frank, and M. Loss, The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space, Math. Res. Lett. 15 (2008), 613-622.
3. K. Bogdan and B. Dyda, The best constant in a fractional Hardy inequality, Math. Nachr. 284 (2011), 629-638.
4. Z.-Q. Chen and T. Kumagai, Heat kernel estimates for stable-like processes on d-sets, Stoch. Process. Appl. 108 (2003), 27-62. (Pubitemid 37155246)
5. E. B. Davies, Spectral Theory and Differential Operators, Cambridge Stud. Adv. Math. 42, Cambridge Univ. Press, Cambridge, 1995.
6. B. Dyda, Fractional Hardy inequality with a remainder term, Colloq. Math. 122 (2011), 59-67.
7. S. Filippas, L. Moschini, and A. Tertikas, Sharp trace Hardy-Sobolev-Maz'ya inequalities and the fractional Laplacian, arXiv:1110.3604v1 [math.AP].
8. R. L. Frank and M. Loss, Hardy-Sobolev-Maz'ya inequalities for arbitrary domains, J. Math. Pures Appl. 97 (2012), 39-54.
9. R. L. Frank and R. Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal. 255 (2008), 3407-3430.
10. R. L. Frank and R. Seiringer, Sharp fractional Hardy inequalities in half-spaces, in: Around the Research of Vladimir Maz'ya. I, Int. Math. Ser. (N.Y.) 11, Springer, New York, 2010, 161-167.
11. A. M. Garsia, E. Rodemich, and H. Rumsey, Jr., A real variable lemma and the continuity of paths of some Gaussian processes, Indiana Univ. Math. J. 20 (1970/1971), 565-578.
12. Q.-Y. Guan and Z.-M. Ma, Reflected symmetric *-stable processes and regional fractional Laplacian, Probab. Theory Related Fields 134 (2006), 649-694. (Pubitemid 43201085)
13. M. Loss and C. Sloane, Hardy inequalities for fractional integrals on general domains, J. Funct. Anal. 259 (2010), 1369-1379.
14. V. G. Maz'ja, Sobolev Spaces, Springer Ser. Soviet Math., Springer, Berlin, 1985.
15. C. A. Sloane, A fractional Hardy-Sobolev-Maz'ya inequality on the upper halfspace, Proc. Amer. Math. Soc. 139 (2011), 4003-4016.