Related papers: Bohr's theorem for Ces\'aro operator and certain i…
We study automorphisms and invariants for the algebra $\mathbb{O}$ of octonions and octonionic slice regular functions $f:\mathbb{O} \to \mathbb{O}$.
The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings…
We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K<R\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any…
We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…
This article focuses on the Bohr radius problem for the derivatives of analytic functions, along with a technique of establishing Bohr inequalities in classical and generalized settings.
In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…
The purpose of this paper is twofold. One is to enrich from a geometrical point of view the theory of octonionic slice regular functions. We first prove a boundary Schwarz lemma for slice regular self-mappings of the open unit ball of the…
In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved Bohr inequality with a certain power of the norm of the…
This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…
The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(\rho, \delta)$ which…
We consider the operator $\sL$ defined on $C^2(\bR^d)$ functions by \sL f(x)&=&{1/2}\sum_{i,j=1}^d a_{ij}(x)\frac{\partial^2f(x)}{\partial x_i\partial x_j}+\sum_{i=1}^d b_i(x)\frac{\partial f(x)}{\partial x_i}…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We establish a version of the Beurling-Pollard theorem for operator synthesis and apply it to derive some results on linear operator equations and to prove a Beurling-Pollard type theorem for Varopoulos tensor algebras. Additionally we…
We say that a class $\mathcal{B}$ of analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if for the largest radius $R_{f}<1$, the…
Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…
In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series…
This article investigates the Bohr phenomenon and sharp coefficient problems for the class $\mathcal{A}_{\beta}$, a subclass of analytic self-maps of the unit disk with the holomorphic generators of one-parameter continuous semigroups. By…
In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr…
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination family of functions, and establish the classical Bohr's inequality for the class of quasisubordinate functions. As a consequence, we improve and obtain…
Let $\mathbb{B}$ be the unit ball of a complex Banach space $X$. In this paper, we will generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball $\mathbb{B}$ by using the radial derivative. Next, we define an…