Related papers: Partitions and functional Santalo inequalities

An inequality of Brascamp-Lieb-Luttinger and of Rogers states that among subsets of Euclidean space $\mathbb{R}^d$ of specified Lebesgue measures, balls centered at the origin are maximizers of certain functionals defined by…

We prove fractional Hardy--Sobolev--Maz'ya inequality for balls and a half-space, partially answering the open problem posed by Frank and Seiringer [arXiv:0906.1561v1 [math.FA], 2009] We note that for half-spaces this inequality has been…

By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…

Here we present ZFC theorems yielding the Halpern-L\a"uchli theorem and avoiding metamathematical notions in their formulations.

We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures.

In this paper, we give a new proof of a result due to Bezivin that a D-finite Mahler function is necessarily rational. This also gives a new proof of the rational-transcendental dichotomy of Mahler functions due to Nishioka. Using our…

In this note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001)…

We define an associated Lindel\"of-function for the ratio of the zeta functions and use its representation to get a unique extension of Lindel\"of's function that proves Lindel\"of's hypothesis.

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow…

Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence…

The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we…

Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…

We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…

The Blaschke Santal\'o inequality and the $L_p$ affine isoperimetric inequalities are major inequalities in convex geometry and they have a wide range of applications. Functional versions of the Blaschke Santal\'o inequality have been…

Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…

We consider the fractional Laplacian operator $(-\Delta)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a…

We prove that the number of partitions of an integer into at most b distinct parts of size at most n forms a unimodal sequence for n sufficiently large with respect to b. This resolves a recent conjecture of Stanley and Zanello.

A version of the recent functional inequality between the Hessians of the square root and the logarithm of positive functions is proven in spaces with non-zero curvature.