A note on Sobolev type trace inequalities for $s$-harmonic extensions

키워드

참고문헌 (17)

1. W. Beckner, "Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality", Ann. of Math. (2), 138(1), pp.213~242 (1993)[DOI]
2. H.-Q. Bui, "A characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels, in Functional analysis, harmonic analysis, and image processing: a collection of papers in honor of Bj¨orn Jawerth", Contemp. Math, 693, pp.109~141 (2017), Amer. Math. Soc[DOI]
3. L. Caffarelli, "Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian", Invent. Math, 171(2), pp.425~461 (2008)[DOI]
4. L. Caffarelli, "An extension problem related to the fractional Laplacian", Comm. Partial Differential Equations, 32(7-9), pp.1245~1260 (2007)[DOI]
5. L. Caffarelli, "Fractional elliptic equations, Caccioppoli estimates and regularity", Ann. Inst. H. Poincar´e C Anal. Non Lin´eaire, 33(3), pp.767~807 (2016)[DOI]
6. L. Caffarelli, "Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation", Ann. of Math. (2), 171(3), pp.1903~1930 (2010)[DOI]
7. G. Dafni, "Some new tent spaces and duality theorems for fractional Carleson measures and Qα(Rn)", J. Funct. Anal, 208(2), pp.377~422 (2004)[DOI]
8. E. Di Nezza, "Hitchhiker’s guide to the fractional Sobolev spaces", Bull. Sci. Math, 136(5), pp.521~573 (2012)[DOI]
9. J. Escobar, "Sharp constant in a Sobolev trace inequality", Indiana Univ. Math. J, 37(3), pp.687~698 (1988)[DOI]
10. R. L. Frank, "Non-linear ground state representations and sharp Hardy inequalities", J. Funct. Anal, 255(12), pp.3407~3430 (2008)[DOI]
11. J. Haddad, "Sharp affine weighted Lp Sobolev type inequalities", Trans. Amer. Math. Soc, 372(4), pp.2753~2776 (2019)[DOI]
12. H. Hajaiej, "Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms", J. Math. Anal. Appl, 396(2), pp.569~577 (2012)[DOI]
13. P. Li, "Fractional Besov trace", extension-type inequalities via the Caffarelli-Silvestre extension, 2022, pp.32(9), 30~
14. J. Merker, "Generalizations of logarithmic Sobolev inequalities", Discrete Contin. Dyn. Syst. Ser. S, 1(2), pp.329~338 (2008)[DOI]
15. V. H. Nguyen, "Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz’ya type inequalities", J. Funct. Anal, 270(11), pp.4117~4151 (2016)[DOI]
16. J. Xiao, "A sharp Sobolev trace inequality for the fractional-order derivatives", Bull. Sci. Math, 130(1), pp.87~96 (2006)[DOI]
17. J. Xiao, "Fractional Sobolev, Moser-Trudinger Morrey-Sobolev inequalities under Lorentz norms", J. Math. Sci. (N.Y.), 166(3), pp.357~376 (2010)[DOI]

관련 논문AI추천