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Rearrangement Inequalities with Application to Ratios of Heat Kernels

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Abstract

We prove rearrangement inequalities for multiple integrals, using the polarization technique. Polarization refers to rearranging a function with respect to a hyperplane. Then we derive sharp inequalities for ratios of integrals of heat kernels of Schrödinger operators, using our polarization inequalities. These ratio inequalities imply inequalities for the partition functions and extend the results of R. Bañuelos, P.J. Méndez-Hernández and D. You.

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Authors and Affiliations

  1. Department of Mathematics, Washington University in St. Louis, St. Louis, MO, 63130, U.S.A.

    Cristina Draghici

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  1. Cristina Draghici
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Correspondence to Cristina Draghici.

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Mathematics Subject Classifications (2000)

26D15, 28A25, 35J10.

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Draghici, C. Rearrangement Inequalities with Application to Ratios of Heat Kernels. Potential Anal 22, 351–374 (2005). https://doi.org/10.1007/s11118-004-1328-5

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  • DOI: https://doi.org/10.1007/s11118-004-1328-5

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