On the multilinear restriction and Kakeya conjectures
Tóm tắt
Từ khóa
Tài liệu tham khảo
Barceló, J.A., Bennett, J.M., Carbery, A.: A multilinear extension inequality in R n . Bull. London Math. Soc. 36, 407–412 (2004)
Beckner, W., Carbery, A., Semmes, S., Soria, F.: A note on restriction of the Fourier transform to spheres. Bull. London Math. Soc. 21, 394–398 (1989)
Bennett, J.: A trilinear restriction problem for the paraboloid in R 3. Electron. Res. Announc. Amer. Math. Soc. 10, 97–102 (2004)
Bennett, J., Carbery, A., Christ, M., Tao, T.: The Brascamp-Lieb inequalities: finiteness, structure and extremals. To appear in Geom. Funct. Anal.
Bennett, J., Carbery, A., Wright, J.: A non-linear generalisation of the Loomis-Whitney inequality and applications. Math. Res. Lett. 12, 443–457 (2005)
Bergh, J., Löfström, J.: Interpolation spaces. An introduction. Springer, Berlin Heidelberg New York (1976)
Blei, R.C.: Fractional Cartesian products of sets. Ann. Inst. Fourier (Grenoble) 29(2), 79–105 (1979)
Bourgain, J.: Besicovitch type maximal operators and applications to Fourier analysis. Geom. Funct. Anal. 1, 147–187 (1991)
Bourgain, J.: L p -estimates for oscillatory integrals in several variables. Geom. Funct. Anal. 1, 321–374 (1991)
Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I, II. Geom. Funct. Anal. 3, 107–156, 209–262 (1993)
Carlen, E.A., Lieb, E.H., Loss, M.: A sharp analog of Young’s inequality on S N and related entropy inequalities. J. Geom. Anal. 14, 487–520 (2004)
Chazelle, B., Edelsbrunner, H., Guibas, L.J., Pollack, R., Seidel, R., Sharir, M., Snoeyink, J.: Counting and cutting cycles of lines and rods in space. Comput. Geom. 1, 305–323 (1992)
Córdoba, A.: Multipliers of $\cal F$ (L p ), in Euclidean Harmonic Analysis (Proc. Sem., Univ. Maryland, College Park, MD, 1979), Lecture Notes in Math, 779, pp. 162–177. Springer, Berlin Heidelberg New York (1980)
Erdogan, M.B.: A bilinear Fourier extension theorem and applications to the distance set problem. Int. Math. Res. Not. 23, 1411–1425 (2005)
Feldman, S., Sharir, M.: An improved bound for joints in arrangements of lines in space. Discrete. Comput. Geom. 33, 307–320 (2005)
Katz, N.H., Laba, I., Tao, T.: An improved bound on the Minkowski dimension of Besicovitch sets in R 3. Ann. Math. 152, 383–446 (2000)
Klainerman, S., Machedon, M.: Space-time estimates for null forms and the local existence theorem. Comm. Pure Appl. Math. 46, 1221–1268 (1993)
Lee, S.: Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators. Duke Math. J. 122, 205–232 (2004)
Loomis, L.H., Whitney, H.: An inequality related to the isoperimetric inequality. Bull. Amer. Math. Soc. 55, 961–962 (1949)
Moyua, A., Vargas, A., Vega, L.: Restriction theorems and maximal operators related to oscillatory integrals in R 3. Duke Math. J. 96, 547–574 (1999)
Oberlin, D.M., Stein, E.M.: Mapping properties of the Radon transform. Indiana Univ. Math. J. 31, 641–650 (1982)
Sharir, M.: On joints in arrangements of lines in space and related problems. J. Combin. Theory Ser. A 67, 89–99 (1994)
Stein, E.M.: Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series, 43. Princeton University Press, Princeton, NJ (1993)
Tao, T.: Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates. Math. Z. 238, 215–268 (2001)
Tao, T.: A sharp bilinear restrictions estimate for paraboloids. Geom. Funct. Anal. 13, 1359–1384 (2003)
Tao, T.: Recent progress on the restriction conjecture. arXiv:math.CA/0311181
Tao, T., Vargas, A., Vega, L.: A bilinear approach to the restriction and Kakeya conjectures. J. Amer. Math. Soc. 11, 967–1000 (1998)
Wolff, T.H.: Recent work connected with the Kakeya problem, in Prospects in Mathematics (Princeton, NJ, 1996), pp. 129–162. Amer. Math. Soc., Providence, RI (1999)