Related papers: On a reverse form of the Brascamp-Lieb inequality
We show that the Brascamp-Lieb (BL) constant BL(-,p) is a semi-algebraic function on the set of feasible data. Consequently, it is algebraic in the sense that it satisfies a polynomial relation of the form P(V, BL(V,p))=0 for a non-zero…
Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp--Lieb data are, in a certain sense, ubiquitous. This addresses a question raised by Bennett and Tao in their recent work on the…
This paper establishes a necessary and sufficient condition for $L^p$-boundedness of a class of multilinear functionals which includes both the Brascamp-Lieb inequalities and generalized Radon transforms associated to algebraic incidence…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
Brezis-Lieb lemma is a refinement of Fatou lemma providing an evaluation of the gap between the integral for a sequence and the integral for its pointwise limit. This note studies the question if such gap can be evaluated when there is no…
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell…
We will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of…
Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by B\"or\"oczky-Lutwak-Yang-Zhang. We name…
In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.
We show a reverse isoperimetric inequality within the class of relative outer parallel bodies, with respect to a general convex body $E$, along with its equality condition. Based on the convexity of the sequence of quermassintegrals of…
In this paper we prove a special case of the Lehmer inequality for Drinfeld modules. Also, based on this inequality, we prove certain Mordell-Weil type of theorems for certain infinitely generated fields.
We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…
In this paper we provide another way to deduce the Loomis-Whitney inequality on higher dimensional Heisenberg groups $\mathbb{H}^n$ based on the one on the first Heisenberg group $\mathbb{H}^1$ and the known nonlinear Loomis-Whitney…
In this work, we extend the well known Brezis-Lieb Lemma to the Orlicz space.
We prove a kind of "reverse Schwarz--Pick lemma" for holomorphic self-maps of the disk. The result becomes especially clear-cut for inner functions and casts new light on their derivatives.
The experiments with broadband down-converted light clearly show inequality of forward and reversed processes in optics.
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).
H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces.…