Distributional and Lq norm inequalities for polynomials over convex bodies in ℝn

Mathematical Research Letters

Volumn 8, Issue 3, 2001, Pages 233-248

  Carbery, Anthony ^a   Wright, James ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035535873     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2001.v8.n3.a1     Document Type: Article

References (11)

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4. [CCW] A. Carbery, M. Christ and J. Wright, Multidimensional van der Corput and sublevel estimates, J. Amer. Math. Soc 12 (1999), 981-1015.
5. [C] H. Cartan, Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, Ann. Sci. École Norm. Sup. 45 (1928), 225-346.
6. [DR] R. M. Dudley and B. Randol, Implications of pointwise bounds on polynomials, Duke Math. J. 29 (1962), 455-458.
7. [GM] M. Gromov and V. D. Milman, Brunn theorem and a concentration of volume for convex bodies, Israel seminar on geometrical aspects of functional analysis (1983/84), Tel Aviv University, Tel Aviv, 1984.
8. [H] W. H. Hayman, Subharmonic Functions, vol. 2, London Mathematical Society Monographs 20, Academic Press, London, 1989.
9. [KLS] R. Kannan, L. Lovász and M. Simonovits, Isoperimetric problems for convex bodies and a localization lemma, Discrete Comput. Geom. 13 (1995), 541-559.
10. [NSV] F. Nazarov, M. Sodin, and A. Volberg, The geometric KLS lemma, dimension-free estimates for the distribution of values of polynomials and distribution of zeroes of random analytic functions, preprint.
11. [RS] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals I: Oscillatory integrals, J. Funct. Anal. 73 (1987), 179-194.