Table of Contents

• Introduction and notations
• Poincaré-type inequalities
• Entropy and Orlicz spaces
• \(\mathbf{LS}_q\) and Hardy-type inequalities on the line
• Probability measures satisfying \(\mathbf{LS}_q\)-inequalities on the real line
• Exponential integrability and perturbation of measures
• \(\mathbf{LS}_q\)-inequalities for Gibbs measures with super Gaussian tails
• \(\mathbf{LS}_q\)-inequalities and Markov semigroups
• Isoperimetry
• The localization argument
• Infinitesimal version
• Proof of Theorem 9.2
• Euclidean distance (proof of Theorem 9.1)
• Uniformly convex bodies
• From isoperimetry to \(\mathbf{LS}_q\)-inequalities
• Isoperimetric functional inequalities
• Bibliography