相关论文: The Muirhead-Rado inequality, 2: Symmetric means a…
We establish a quantitative isoperimetric inequality for weighted Riemannian manifolds with $\mathrm{Ric}_{\infty} \ge 1$. Precisely, we give an upper bound of the volume of the symmetric difference between a Borel set and a sub-level (or…
We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by \cite{AFV} in Euclidean context. Also we discuss the…
We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie groups and graphs.
In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…
In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.
A mixed arithmetic-mean, geometric-mean inequality was conjectured by F. Holland and proved by K. Kedlaya. In this note, we prove a mixed arithmetic-mean, harmonic-mean inequality and a mixed geometric-mean, harmonic-mean, and a more…
This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…
Given $\alpha >0$, we establish the following two supercritical Moser-Trudinger inequalities \[ \sup\limits_{u \in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\big( (\alpha_n + |x|^\alpha) |u|^{\frac{n}{n-1}} \big)…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
Using elementary techniques, we prove sharp anisotropic Hardy-Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by F. Bayart in 2018.
In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
The two-weight inequality for the Hilbert transform is characterized for an arbitrary pair of positive Radon measures $\sigma$ and $w$ on $\mathbb R$. In particular, the possibility of common point masses is allowed, lifting a restriction…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
The aim of this paper is to provide a proof for a version of Morse inequality for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof…
This article presents extensions of the Cram{\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions…
Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian measures. Unlike in the classical Brunn-Minkowski theory, the…
Equivalencies of many basic elementary inequalities are given
New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex.…