Related papers: A Hardy-Moser-Trudinger inequality

A Sobolev type embedding for radially symmetric functions on the unit ball $B$ in $\mathbb R^n$, $n\geq 3$, into the variable exponent Lebesgue space $L_{2^\star + |x|^\alpha} (B)$, $2^\star = 2n/(n-2)$, $\alpha>0$, is known due to J.M. do…

We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some properties of such a constant, as well as of the associated variational problem. We then…

In the Euclidean space $\mathbb{R}^d$, the sharp classical Sobolev inequality is equivalent by conformal invariance to a Sobolev inequality on the hyperbolic space $\mathbb{H}^d$. This inequality is sharp in dimension $d\geq 4$, but it is…

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…

We derive sharp Adams inequalities for the Riesz and other potentials of functions with arbitrary compact support in R^n. Up to now such results were only known for a class of functions whose supports have uniformly bounded measure. We…

We prove that if $M$ is a closed $n$-dimensional Riemannian manifold, $n \ge 3$, with ${\rm Ric}\ge n-1$ and for which the optimal constant in the critical Sobolev inequality equals the one of the $n$-dimensional sphere $\mathbb{S}^n$, then…

We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case $sp=d$, where $p>1, ~ s \in (0,1)$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$. In particular, we establish…

In this article, we investigate the quantitative form of the classical Hardy inequality. In our first result, we prove the following quantitative bound under the assumption that the $\mathbb{M}^N$ is a Riemannian model satisfying the…

The classical Bohr inequality states that if $ f $ is an analytic function with the power series representation $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $ such that $ |f(z)|\leq 1 $ for…

We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, which converges to the critical Hardy inequality. Sobolev type…

\begin{abstract} In this paper we state the following weighted Hardy type inequality for any functions $\varphi$ in a weighted Sobolev space and for weight functions $\mu$ of a quite general type \begin{equation*} c_{N,\mu}…

We prove a set of inequalities that interpolate the Cauchy-Schwarz inequality and the triangle inequality. Every nondecreasing, convex function with a concave derivative induces such an inequality. They hold in any metric space that…

Let $p>1$. The Harnack inequality and H\"older continuity for $p$-harmonic functions in bounded domains in $\mathbb{R}^d$ are usually proved via Moser iteration. In 2013 Luiro, Parviainen and Saksman showed that tug-of-war games can also be…

A classical result due to Frank and Seiringer asserts that for $1\leq p<\frac Ns$, there exists a sharp constant $\mathcal{C}_{N,s,p}>0$ such that $$…

Extending several works, we prove a general Adams-Moser-Trudinger type inequality for the embedding of Bessel-potential spaces $\tilde H^{\frac{n}{p},p}(\Omega)$ into Orlicz spaces for an arbitrary domain $\Omega\subset \mathbb{R}^n$ with…

The classical Poincar\'e inequality establishes that for any bounded regular domain $\Omega\subset \R^N$ there exists a constant $C=C(\Omega)>0$ such that $$ \int_{\Omega} |u|^2\, dx \leq C \int_{\Omega} |\nabla u|^2\, dx \ \ \forall u \in…

Given $N\geq 3,$ we consider the critical Hardy-Sobolev equation $-\Delta u-\frac{\gamma}{|x|^2}u=\frac{|u|^{2^*(s)-2}u}{|x|^s}$ in $\mathbb{R}^N\setminus \{0\},$ where $0<\gamma<\gamma_{H}:=\left(\frac{N-2}{2}\right)^2,\,s\in (0,2)$ and…

We introduce the concept of Calder\'on-Zygmund inequalities on Riemannian manifolds. For $1<p<\infty$, these are inequalities of the form $$ \left\Vert \mathrm{Hess}\left( u\right) \right\Vert _{L^p}\leq C_{1}\left\Vert u\right\Vert…

The classical Beurling-Helson-Lowdenslager theorem characterizes the shift-invariant subspaces of the Hardy space $H^{2}$ and of the Lebesgue space $L^{2}$. In this paper, which is self-contained, we define a very general class of norms…

In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and…