Related papers: Sharp operator mean inequalities of the numerical …
The main goal of this article is to establish several new upper and lower bounds for the $\mathbb{A}$-numerical radius of $2\times 2$ operator matrices, where $\mathbb{A}$ be the $2\times 2$ diagonal operator matrix whose diagonal entries…
This paper establishes new upper bounds for the $A$-numerical radius of operator matrices in semi-Hilbertian spaces by leveraging the $A$-Buzano inequality and developing refined techniques for operator matrices. We present several sharp…
In this paper, we study the numerical range of Jacobi operators and it is shown that under certain conditions, the boundary of the numerical range of these operators can be non-round only at the points where it touches the essential…
We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…
Two sharp comparison results are derived for three-dimensional complete noncompact manifolds with scalar curvature bounded from below. The first one concerns the Green's function. When the scalar curvature is nonnegative, it states that the…
It is known that the function $f(e^x)/g(e^x)$ is positive definite for some functions $f,g$ implies the operator norm inequality related to $f,g$. We treat functions which have the following form: $f(t) = t^{(1-\sum_{i=1}^n…
We prove a sharp analog of Young's inequality on $S^N$, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This…
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…
We study the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on…
For $0\leq \alpha <1$, the sharp radii of starlikeness and convexity of order $\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\leq b\leq 1$, and $|a_n|\leq n…
We prove a sharpened version of the Strichartz inequality for radial solutions of the Schr\"odinger equation in $\mathbb{R}^2\times \mathbb{R}$. We establish an improved upper bound for functions that nearly extremize the inequality, with a…
We prove that the Hardy-Littlewood maximal operator is discontinuous on $\bmorn$ and maps $\vmorn$ to itself. A counterexample to boundedness of the strong and directional maximal operators on $\bmorn$ is given, and properties of slices of…
Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…
This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{D}^n$. We establish a sharp extension of the classical Bohr…
In this paper we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fej\'er means in this subspace is bounded from the Hardy space $H_{p}$ to the space $L_{p}$ for all $0<p\leq 1/2.$ Moreover, we…
In this paper, we give sharp Rusak- and Markov-type inequalities for rational functions on several intervals when the system of intervals is a \textquotedblleft rational function inverse image\textquotedblright\, of an interval and those…
We show that the lowest constant appearing in the weak type (1,1) inequality satisfied by the centered Hardy-Littlewood maximal operator on radial integrable functions is 1.
We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.