相关论文: Several analytic inequalities in some $Q-$spaces
For the sequence of multi-indexes $\{\alpha_i\}_{i=1}^{m}$ and $\beta$ we study the inequality \[ \|D^{\beta} f\|_{L_1(\mathbb{T}^d)}\leq K_N \sum_{j= 1}^{m} \|D^{\alpha_j}f\|_{L_1(\mathbb{T}^d)}, \] where $f$ is a trigonometric polynomial…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form $S_N=\sum_{n=1}^N (F(\xi_{q_1(n)},\xi_{q_2(n)},...,\xi_{q_\ell(n)})-\bar F)$.
We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to…
In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball…
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
Let $p\in[1,\infty]$, $q\in(1,\infty)$, $s\in\mathbb{Z}_+:=\mathbb{N}\cup\{0\}$, and $\alpha\in\mathbb{R}$. In this article, the authors introduce a reasonable version $\widetilde T$ of the Calder\'on--Zygmund operator $T$ on…
We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.
First and second-order inequalities of Friedrichs type for Sobolev functions in arbitrary domains are offered. The relevant inequalities involve optimal norms and constants that are independent of the geometry of the domain. Parallel…
We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than -1. Without symmetry assumption, it…
In this paper, we are concerned with the critical and subcritical Trudinger-Moser type inequalities for functions in a fractional Sobolev space $H^{1/2,2}$ on the whole real line. We prove the relation between two inequalities and discuss…
In this paper, we genelize the Heintze-Karcher type inequalities for fractional Q-curvature $Q_{2\gamma}$ on conformally compact Einstein manifolds. Such inequality holds for all $\gamma\in (0,1]$. In particular, for $\gamma=\frac{1}{2}$…
Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
The paper provides weighted Sobolev inequalities of the Caffarelli-Kohn-Nirenberg type for functions with multi-radial symmetry. Similarly to the previously studied radial case, the range of parameters in CKN inequalities can be extended,…
We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}$ in the unit disk. Later, we establish the Bohr-type operator on analytic functions…
In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.