Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
classification
🧮 math.FA
keywords
inequalityinversefunctionallogarithmicsobolevaffineaffine-isoperimetryentropy
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We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincar'e inequality for the Gaussian measure.
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