相关论文: A Minkowski Type Trace Inequality and Strong Subad…

We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from…

$L_p$ Brunn-Minkowski type inequa\-li\-ties for the lattice point enumerator $\mathrm{G}_n(\cdot)$ are shown, both in a geometrical and in a functional setting. In particular, we prove that \[\mathrm{G}_n\bigl((1-\lambda)\cdot K +_p…

We study traces of weighted Triebel-Lizorkin spaces $F^s_{p,q}({\mathbb R}^n,w)$ on hyperplanes ${\mathbb R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight $w_\alpha(x) = |x_n|^\alpha$ when $|x_n|\leq…

The Pinsker subgroup of an abelian group with respect to an endomorphism was introduced in the context of algebraic entropy. Motivated by the nice properties and characterizations of the Pinsker subgroup, we generalize its construction in…

We study properties of the boundary trace operator on the Sobolev space $W^1_1(\Omega)$. Using the density result by Koskela and Zhang, we define a surjective operator \mbox{$Tr: W^1_1(\Omega_K)\rightarrow X(\Omega_K)$}, where $\Omega_K$ is…

Let $S$ be a compact, orientable surface of hyperbolic type. Let $(k_+,k_-)$ be a pair of negative numbers and let $(g_+, g_-)$ be a pair of marked metrics over $S$ of constant curvature equal to $k_+$ and $k_-$ respectively. Using a…

In this paper, we obtain the subadditivity inequality of strongly operator convex functions on $(0, \infty)$ and $(-\infty,0)$. Applying the properties of operator convex functions, we deduce the subadditivity property of operator monotone…

A Minkowski symmetral of an $\alpha$-concave function is introduced, and some of its fundamental properties are derived. It is shown that for a given $\alpha$-concave function, there exists a sequence of Minkowski symmetrizations that…

We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present converse of Ando's inequality, for each parameter. We give examples to compare our results with the known…

A sharp quantitative version of the $L_p-$mixed volume inequality is established. This is achieved by exploiting an improved Jensen inequality. This inequality is a generalization of Pinsker-Csisz\'ar-Kullback inequality for the Tsallis…

In this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set $\Omega \subset \mathbb R^n$, $n\geq 3$. Our proof relies on the discovery of effective monotonicity formulas holding along the…

In this note we consider a certain class of convolution operators acting on the L_p spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the subspace of functions with mean zero.

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…

We prove some refinements of a reverse AM-GM operator inequality due to M. Lin [Studia Math. 2013;215:187-194]. In particular, we show the operator inequality \begin{eqnarray*} \Phi^p\left(A\nabla_\nu B+2rMm(A^{-1}\nabla B^{-1}-A^{-1}\sharp…

Let $K_1, K_2$ be two compact convex sets in $\mathit{C}$. Their Minkowski product is the set $K_1K_2 = \{ab: a \in K_1, b\in K_2\}$. We show that the set $K_1K_2$ is star-shaped if $K_1$ is a line segment or a circular disk. Examples for…

We characterize the entropy and minimax risk of a broad class of compact pseudodifferential operators. Under suitable decay and regularity conditions on the symbol, we combine a Weyl-type asymptotic relation between the eigenvalue-counting…

We show that, given a closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_n\to\infty$ with the following property: if $T$ is a Hilbert-space contraction such that $\sigma(T)\subset E$ and…

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general…

We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…

The classical Hlawka inequality possesses deep connections with zonotopes and zonoids in convex geometry, and has been related to Minkowski space. We introduce Hlawka Type-1 and Type-2 quantities, and establish a Hlawka-type relation…