Related papers: Reverse Holder, Minkowski, And Hanner Inequalities…
We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…
The M\"obius invariant space $\mathcal{Q}_p$, $0<p<\infty$, consists of functions $f$ which are analytic in the open unit disk $\mathbb{D}$ with $$ \|f\|_{\mathcal{Q}_p}=|f(0)|+\sup_{w\in \D} \left(\int_\D |f'(z)|^2(1-|\sigma_w(z)|^2)^p…
Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big)…
We prove sharp $L^p(w)$ norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the $A_p$ characteristic of $w$ for all $1<p<\infty$. This implies the same sharp inequalities for the classical…
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…
The Brunn-Minkowski Theorem asserts that $\mu_d(A+B)^{1/d}\geq \mu_d(A)^{1/d}+\mu_d(B)^{1/d}$ for convex bodies $A,\,B\subseteq \R^d$, where $\mu_d$ denotes the $d$-dimensional Lebesgue measure. It is well-known that equality holds if and…
Inspired by the work of Cossetti and D'Arca [CD25], we show that the general weighted $L^{p}$-Hardy type inequalities [CD25, Theorems 1.1 and 1.2] and the corresponding identities hold for all $1<p<\infty$, thus extending their results…
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
A matrix $P$ is said to be a nontrivial generalized reflection matrix over the real quaternion algebra $\mathbb{H}$ if $P^{\ast }=P\neq I$ and $P^{2}=I$ where $\ast$ means conjugate and transpose. We say that $A\in\mathbb{H}^{n\times n}$ is…
The M-P (Moore-Penrose) pseudoinverse has as a key application the computation of least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given input matrix is sparse, its M-P pseudoinverse can be…
We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the $\Gamma$-calculus a la Bakry et al, we show the…
We consider the problem of approximation of matrix functions of class $L^p$ on the unit circle by matrix functions analytic in the unit disk in the norm of $L^p$, $2\le p<\be$. For an $m\times n$ matrix function $\Phi$ in $L^p$, we consider…
We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in…
In this work, the mixed Schwarz inequality for semi-Hilbertian space operators is proved. Namely, for every positive Hilbert space operator $A$. If $f$ and $g$ are nonnegative continuous functions on $\left[0,\infty\right)$ satisfying…
Let $M=(0,\infty)_r\times Y$ be a $d$-dimensional ($d\ge 3$) metric cone with metric<br/>$g=dr^2+r^2h$, where $(Y,h)$ is a closed Riemannian manifold. Let<br/>$H=\Delta+V_0/r^2$ be the associated Schrodinger operator, with<br/>$V_0\in…
Inequalities for the transformation operator kernel $A(x,y)$ in terms of $F$-function are given, and vice versa. These inequalities are applied to inverse scattering on half-line. Characterization of the scattering data corresponding to the…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*}…