Related papers: On a reverse form of the Brascamp-Lieb inequality
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
We prove a family of sharp multilinear integral inequalities on real spheres involving functions that possess some symmetries that can be described by annihilation by certain sets of vector fields. The Lebesgue exponents involved are seen…
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
Recently a new proof was given for Beurling's Ingham type theorem on one-dimensional nonharmonic Fourier series, providing explicit constants. We improve this result by applying a short elementary method instead of the previous complex…
We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.
We initiate the study of a duality theory which applies to norm inequalities for pointwise weighted geometric means of positive operators. The theory finds its expression in terms of certain pointwise factorisation properties of function…
The celebrated Brascamp-Lieb (BL) inequalities (and their extensions) are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory. While their structural theory is…
We prove a range of $L^p$ bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We…
In \cite{Nam} Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with…
In this paper, we first provide a better estimate of the second inequality in Hermite-Hadamard inequality. Next, we study the reverse of the celebrated Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for…
Some new reverses of the Cauchy-Bunyakovsky-Schwarz inequality for n-tuples of real and complex numbers related to Cassels and Shisha-Mond results are given.
Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
In this article we derive a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying supported boundary conditions. To this end, we combine the use of a suitable conformal mapping which…
The Riesz-Sobolev inequality provides an upper bound, in integral form, for the convolution of indicator functions of subsets of Euclidean space. We formulate and prove a sharper form of the inequality. This can be equivalently phrased as a…
In this paper, we continue to study some applications with respect to a Reilly type integral formula associated with the $\phi$-Laplacian. Some inequalities of Brascamp-Lieb type and Colesanti type are provided.
Three equivalent characterizations of probability measures through independence criteria are given. These characterizations lead to a family of Brascamp--Lieb-type inequalities for relative entropy, determine equilibrium states and sharp…