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Title of Journal: Potential Anal

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Abbravation: Potential Analysis

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Springer Netherlands

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10.1007/bf02936041

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1572-929X

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Functional Inequalities and Hamilton–Jacobi Equati

Authors: Zoltán M Balogh Alexandre Engulatov Lars Hunziker Outi Elina Maasalo
Publish Date: 2011/04/28
Volume: 36, Issue: 2, Pages: 317-337
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Abstract

We study the connection between the pTalagrand inequality and the qlogarithmic Sololev inequality for conjugate exponents p ≥ 2 q ≤ 2 in proper geodesic metric spaces By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup Our results generalize those of Lott and Villani They can be applied to deduce the pTalagrand inequality in the subRiemannian setting of the Heisenberg groupZ M Balogh was supported by the Swiss Nationalfond EC Project GALA “SubRiemannian geometric analysis in Lie groups” and ERC Project HCAA “Harmonic and complex analysis and applications” while A Engulatov and O E Maasalo were supported by the EC Project GALA “SubRiemannian geometric analysis in Lie groups”

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Other Papers In This Journal:
  1. Maximal Inequalities of the Itô Integral with Respect to Poisson Random Measures or Lévy Processes on Banach Spaces
  2. Approximation of Invariant Measures for Regime-switching Diffusions
  3. Brownian Motion and the Distance to a Submanifold
  4. Stability for Parabolic Quasiminimizers
  5. Complementability of Spaces of Harmonic Functions
  6. Equilibrium Diffusion on the Cone of Discrete Radon Measures
  7. Global Heat Kernel Estimates for Symmetric Markov Processes Dominated by Stable-Like Processes in Exterior C 1, η Open Sets
  8. Intertwining Relations for One-Dimensional Diffusions and Application to Functional Inequalities
  9. Integrals Along Rough Paths via Fractional Calculus
  10. Mosco Type Convergence of Bilinear Forms and Weak Convergence of n -Particle Systems
  11. Remarks on a Constrained Optimization Problem for the Ginibre Ensemble
  12. On Calabi’s Strong Maximum Principle via Local Semi-Dirichlet Forms
  13. On States of Total Weighted Occupation Times of a Class of Infinitely Divisible Superprocesses on a Bounded Domain
  14. Uniqueness for Integro-PDE in Hilbert Spaces
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