539 citations · 6.8k across the 160 of their papers we have counts for
13 papers · 1 filter
On the convolution inequality
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb +1
We consider the inequality for real integrable functions on dimensional Euclidean space where denotes the convolution of with itself. We s…
Inequalities that sharpen the triangle inequality for sums of functions in
Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
We study inequalities that sharpen the triangle inequality for sums of functions in .
Inequalities for -norms that sharpen the triangle inequality and complement Hanner's Inequality
Eric A. Carlen, Rupert L. Frank, Paata Ivanisvili +1
In 2006 Carbery raised a question about an improvement on the naïve norm inequality for two functions in of any measure spac…
A dual form of the sharp Nash inequality and its weighted generalization
Eric A. Carlen, Elliott H. Lieb
The well known duality between the Sobolev inequality and the Hardy-Littlewood-Sobolev inequality suggests that the Nash inequality could also have an interesting dual form, even t…
A smooth, complex generalization of the Hobby-Rice theorem
Oleg Lazarev, Elliott H. Lieb
The Hobby-Rice Theorem states that, given functions on , there exists a multiplier such that the integrals of are all simultaneously zero. This…
Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures
Eric A. Carlen, Dario Cordero-Erausquin, Elliott H. Lieb
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of th…
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group…
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and t…
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing…
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices
Eric A. Carlen, Elliott H. Lieb
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We giv…
Brascamp-Lieb Inequalities for Non-Commutative Integration
Eric A. Carlen, Elliott H. Lieb
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.
A Sharp analog of Young's Inequality on and Related Entropy Inequalities
Eric Carlen, Elliott Lieb, Michael Loss
We prove a sharp analog of Young's inequality on , and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives tri…
Poincare Inequalities in Punctured Domains
Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
The classic Poincare inequality bounds the -norm of a function in a bounded domain in terms of some -norm of its gradient in . We generalize this i…