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Related papers: Bohr inequalities for certain integral operators

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In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable…

Classical Analysis and ODEs · Mathematics 2014-01-27 Hua Wang

In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given.

Complex Variables · Mathematics 2015-06-15 Pengtao Li , junming Liu , Zengjian Lou

The concept of Bohr radius for the class of bounded analytic functions was introduced by Harald Bohr in 1914. His initial result received greater interest and was sharpened-refined-generalized by several mathematicians in various…

Complex Variables · Mathematics 2021-04-14 Saminathan Ponnusamy , Ramakrishnan Vijayakumar , Karl-Joachim Wirths

The Bohr theorem states that any function $f(z) = \sum_{n=0}^{\infty} a_{n} z^{n}$, analytic and bounded in the open unit disk, obeys the inequality $\sum_{n=0}^{\infty} |a_{n}| |z|^{n} < 1$ in the open disk of radius 1/3, the so-called…

Complex Variables · Mathematics 2010-04-09 J. Morais , K. Guerlebeck

In this note we prove a class of sharp inequalities for singular integral operators in weighted Lebesgue spaces with angular integrability.

Analysis of PDEs · Mathematics 2016-02-16 Federico Cacciafesta , Renato Lucà

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators…

Functional Analysis · Mathematics 2021-12-07 Ari Laptev , Lukas Schimmer

The present article concerns the Bohr radius for $K$-quasiconformal sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ for which the analytic part $h$ is subordinated to some analytic function $\varphi$, and…

Complex Variables · Mathematics 2019-05-27 ZhiHong Liu , Saminathan Ponnusamy

In this paper, we will study $n$-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg groups and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $n$-dimensional…

Classical Analysis and ODEs · Mathematics 2023-04-25 Zhongci Hang , Xiang Li , Dunyan Yan

Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…

Functional Analysis · Mathematics 2022-06-28 Fuad Kittaneh , Hamid Reza Moradi , Mohammad Sababheh

The boundedness of compactness of integral-type operators from Hardy space to Bloch space on the upper half-plane $\Pi_+=\{z\in\mathbb{C}:Imz>0\}$ are characterized.

Complex Variables · Mathematics 2012-12-10 Xu Ning

We provide a simple unified approach to obtain (i) Discrete polygonal isoperimetric type inequalities of arbitrary high order. (ii) Arbitrary high order isoperimetric type inequalities for smooth curves, where both upper and lower bounds…

Classical Analysis and ODEs · Mathematics 2023-12-27 Kwok-Kun Kwong

A Bernstein-type inequality in the standard Hardy space H^{2} of the unit disc \mathbb{D}=\{z\in\mathbb{C}:\,|z|<1\}, for rational functions in \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D}, 0

Functional Analysis · Mathematics 2011-03-28 Rachid Zarouf

In this work, a pre-Gr\"{u}ss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound…

Functional Analysis · Mathematics 2018-11-21 Mohammad W. Alomari

Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.

Functional Analysis · Mathematics 2007-05-23 Sever Silvestru Dragomir

This paper introduces the second Bohr radius for vector-valued holomorphic functions defined on arbitrary complete Reinhardt domains. We aim to establish the lower and upper bounds of the second Bohr radius in both finite and…

Complex Variables · Mathematics 2025-10-10 Vibhuti Arora , Vinayak M

Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schr\"odinger operators in bounded intervals.

Mathematical Physics · Physics 2021-05-17 Vanderléa R. Bazao , Túlio O. Carvalho , César R. de Oliveira

In this note we show that a sharp rigidity estimate and a sharp Korn's inequality for matrix-valued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due…

Analysis of PDEs · Mathematics 2020-09-18 Sergio Conti , Adriana Garroni

We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in the unit disk.

Complex Variables · Mathematics 2025-07-08 Leonid V. Kovalev

Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and…

Differential Geometry · Mathematics 2020-08-18 Kwok-Kun Kwong , Hojoo Lee

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…

Complex Variables · Mathematics 2011-08-30 V. Ravichandran