Rearrangement inequalities with application to ratios of heat kernels

Potential Analysis

Volumn 22, Issue 4, 2005, Pages 351-374

  Draghici, Cristina ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

Heat kernels; Integral inequality; Rearrangement; Symmetrization

Indexed keywords

EID: 15444371014     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11118-004-1328-5     Document Type: Article

References (25)

1. Almgren, F.J., Jr. and Lieb, E.H.: 'Symmetric decreasing rearrangement is sometimes continuous', J. Amer. Math. Soc. 2(4) (1989), 683-773.
2. Baernstein II, A.: 'Convolution and rearrangement on the circle', Complex Variables Theory Appl. 12(1-4) (1989), 33-37.
3. Baernstein II, A.: 'A unified approach to symmetrization', in A. Alvino et al. (eds.), Partial Differential Equations of Elliptic Type, Symposia Mathematica 35, Cambridge Univ. Press, 1995, pp. 47-91.
4. Baernstein II, A. and Taylor, B.A.: 'Spherical rearrangements, subharmonic functions, and *-functions in n-space", Duke Math. J. 43(2) (1976), 245-268.
5. Bañuelos, R. and Méndez-Hernandéz, P.: 'Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps', J. Funct. Anal. 176 (2000), 368-399.
6. n', Proc. Nat. Acad. Sci. U.S.A. 89(11) (1992), 4816-4819.
7. Brascamp, H.J., Lieb, E.H. and Luttinger, J.M.: 'A general rearrangement inequality for multiple integrals', J. Funct. Anal. 17 (1974), 227-237.
8. Brock, F.: 'A general rearrangement inequality à la Hardy-Littlewood', J. Inequal. Appl. 5(4) (2000), 309-320.
9. Brock, F. and Solynin, A.Y.: 'An approach to symmetrization via polarization', Trans. Amer. Math. Soc. 352(4) (2000), 1759-1796.
10. Burchard, A. and Schmuckenschläger, M.: 'Comparison theorems for exit times', Geom. Funct. Anal. 11(4) (2001), 651-692.
11. Christ, M.: 'Estimates for the k-plane transform', Indiana Univ. Math. J. 33(6) (1984), 891-910.
12. Draghici, C.: 'Polarization and rearrangement inequalities for multiple integrals', PhD Thesis, Washington University, St. Louis, 2003.
13. Folland, G.B.: Real Analysis, Pure and Applied Mathematics, Modern Techniques and Their Applications, Wiley Interscience, New York, 1984.
14. Hardy, G.H., Littlewood, J.E. and Pólya, G.: 'Some simple inequalities satisfied by convex functions', Mess. Math. 58 (1929), 145-152.
15. Hardy, G.H., Littlewood, J.E. and Pólya, G.: Inequalities, Cambridge Mathematical Library, Reprint of the 1952 edn, Cambridge Univ. Press, Cambridge, 1988.
16. Lieb, E.H. and Loss, M.: Analysis, Graduate Studies in Mathematics 14, 2nd edn, Amer. Math. Soc., Providence, RI, 2001.
17. Luttinger, J.M.: 'Generalized isoperimetric inequalities', J. Math. Phys. 14 (1973), 586-593.
18. Luttinger, J.M.: 'Generalized isoperimetric inequalities II, III', J. Math. Phys. 14 (1973), 1444-1447, 1448-1450.
19. Marshall, A.W. and Olkin, I.: Inequalities: Theory of Majorization and its Applications, Mathematics in Science and Engineering 143, Academic Press, New York, 1979.
20. Morpurgo, C.: 'Sharp inequalities for functional integrals and traces of conformally invariant operators', Duke Math. J. 114(3) (2001), 477-554.
21. Pólya, G. and Szegö, G.: Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies 27, Princeton Univ. Press, Princeton, NJ, 1951.
22. Osserman, R.: 'The isoperimetric inequality', Bull. Amer. Math. Soc. 84(6) (1978), 1182-1238.
23. Pfiefer, R.E.: 'Maximum and minimum sets for some geometric mean values', J. Theoret. Probab. 3(2) (1990), 169-179.
24. van den Berg, M.: 'On condensation in the free-boson gas and the spectrum of the Laplacian', J. Statist. Phys. 31(3) (1983), 623-637.
25. You, D.: 'Sharp inequalities for ratios and partition functions of Schrödinger operators', Potential Anal. 18(3) (2001), 219-250, 2003.