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Positive solutions of a fourth-order boundary value problem involving derivatives of all orders
Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions
| 1. | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| 2. | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Airess, Argentina, Argentina |
References:
| [1] |
J. F. Bonder and J. Dolbeault, work in progress, work in progress., ().
|
| [2] |
L. Caffarelli, R. Kohn and L. Nirenberg, First order interpolation inequalities with weights, Compositio Math., 53 (1984), 259-275. |
| [3] |
F. Catrina and Z-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math., 54 (2001), 229-258.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
| [4] |
P. L. De Nápoli, I. Drelichman and R. G. Durán, On weighted inequalities for fractional integrals of radial functions,, To appear in Illinois J. Math. \arXiv{0910.5508}., ().
|
| [5] |
L. Grafakos, "Classical and Modern Fourier Analysis," Pearson Education, Inc., Upper Saddle River, NJ, 2004. |
| [6] |
E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math., 118 (1983), 349-374.
doi: 10.2307/2007032. |
| [7] |
E. M. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970. |
| [8] |
E. M. Stein and G. Weiss, Fractional integrals on $n$-dimensional Euclidean space, J. Math. Mech., 7 (1958), 503-514. |
show all references
References:
| [1] |
J. F. Bonder and J. Dolbeault, work in progress, work in progress., ().
|
| [2] |
L. Caffarelli, R. Kohn and L. Nirenberg, First order interpolation inequalities with weights, Compositio Math., 53 (1984), 259-275. |
| [3] |
F. Catrina and Z-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math., 54 (2001), 229-258.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
| [4] |
P. L. De Nápoli, I. Drelichman and R. G. Durán, On weighted inequalities for fractional integrals of radial functions,, To appear in Illinois J. Math. \arXiv{0910.5508}., ().
|
| [5] |
L. Grafakos, "Classical and Modern Fourier Analysis," Pearson Education, Inc., Upper Saddle River, NJ, 2004. |
| [6] |
E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math., 118 (1983), 349-374.
doi: 10.2307/2007032. |
| [7] |
E. M. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970. |
| [8] |
E. M. Stein and G. Weiss, Fractional integrals on $n$-dimensional Euclidean space, J. Math. Mech., 7 (1958), 503-514. |
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