A sharp Blaschke-Santal inequality for alpha-concave functions

作者：Rotem Liran^*

来源：Geometriae Dedicata, 2014, 172(1): 217-228.

DOI：10.1007/s10711-013-9917-3

• Blaschke-Santalo inequality
• Convexity
• alpha-Concavity
• Log-concavity

We define a new transform on -concave functions, which we call the -transform. Using this new transform, we prove a sharp Blaschke-Santal inequality for -concave functions, and characterize the equality case. This extends the known functional Blaschke-Santal inequality of Artstein-Avidan, Klartag and Milman, and strengthens a result of Bobkov. Finally, we prove that the -transform is a duality transform when restricted to its image. However, this transform is neither surjective nor injective on the entire class of -concave functions.

• 出版日期2014-10