5 papers
On cost-induced Santaló-type inequalities in Polish measure spaces
Dylan Langharst, Andreas Malliaris, Michael Roysdon
We introduce a framework for establishing Blaschke-Santaló-type inequalities on -tuples of Polish measure spaces coupled together by a continuous cost function. Central to our a…
Quantitative improvements of functional inequalities under concavity properties
Andreas Malliaris, Francisco Marín Sola
A classical result of Hensley provides a sharp lower bound for the functional , where is a non-negative, even log-concave function. In the context of stud…
Functional Liftings of Restricted Geometric Inequalities
Andreas Malliaris, James Melbourne, Cyril Roberto +1
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from th…
Monotonicity of functionals associated to product measures via their Fourier transform and applications
Andreas Malliaris
Let be a probability measure on . We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rang…
Curvature and Other Local Inequalities in Markov Semigroups
Devraj Duggal, Andreas Malliaris, James Melbourne +1
Inspired by the approach of Ivanisvili and Volberg towards functional inequalities for probability measures with strictly convex potentials, we investigate the relationship between…