Related papers: Bohr's theorem for Ces\'aro operator and certain i…

The principal aim of this paper is to employ Bessel-type operators in proving the inequality \begin{align*} \int_0^\pi dx \, |f'(x)|^2 \geq \dfrac{1}{4}\int_0^\pi dx \, \dfrac{|f(x)|^2}{\sin^2 (x)}+\dfrac{1}{4}\int_0^\pi dx \,…

Given a compact of ${\bf R}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\bf R}^n$ to the whole of…

This paper mainly uses the nonnegative continuous function $\{\zeta_n(r)\}_{n=0}^{\infty}$ to redefine the Bohr radius for the class of analytic functions satisfying $\real f(z)<1$ in the unit disk $|z|<1$ and redefine the Bohr radius of…

Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…

On the sets of $2\pi$-periodic functions $f$, which are defined with a help of $(\psi, \beta)$-integrals of the functions $\varphi$ from $L_{1}$, we establish Lebesgue-type inequalities, in which the uniform norms of deviations of Fourier…

In the slice Hardy space over the unit ball of quaternions, we introduce the slice hyperbolic backward shift operator $\mathcal S_a$ with the decomposition process $$f=e_a\langle f, e_a\rangle+B_{a}*\mathcal S_a f,$$ where $e_a$ denotes the…

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H\"ormander symbol classes $S^m_{\rho,\delta}$ for all…

The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…

Let $\mathcal{H}=-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}}$ is the full laplacian on $\mathbb{H}^n$ and $V$ is a positive smooth potential, bounded below and…

In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = \lambda y$, where $q \in L^2(0,\pi)$. We prove that if $\|q\|_2$ is sufficiently small, the two spectra corresponding to…

Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is…

We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…

In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…

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…

In this article, we study the Bohr operator for the operator valued subordination class $S(f)$ consisting of holomorphic functions subordinate to $f$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$, where $f:\mathbb{D}…

In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…

In this paper we study ``Bergman-type'' singular integral operators on Ahlfors regular metric spaces. The main result of the paper demonstrates that if a singular integral operator on a Ahlfors regular metric space satisfies an additional…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

We extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…

We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…