Motivated by a problem of scattering theory, the authors solve by quadratures a vector Riemann– Hilbert problem with the matrix coefficient of Chebotarev–Khrapkov type. The problem of matrix factorization reduces to a scalar Riemann–Hilbert boundary-value problem on a twosheeted Riemann surface of genus 3 that is topologically equivalent to a sphere with three handles. The conditions quenching ...

* Correspondence: bcyang@gdei. edu.cn Department of Mathematics, Guangdong University of Education Guangzhou, Guangdong 510303, P. R. China Full list of author information is available at the end of the article Abstract Using the way of weight functions and the technique of real analysis, a half-discrete Hilbert-type inequality with a general homogeneous kernel is obtained, and a best extension...

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, give necessary and sufficient conditions for weighted to be true. The main tool in our proof is continuous Minkowski inequality. addition, present some consequences obtained homogeneous groups, hyperbolic spaces Cartan-Hadamard manifolds.&#x0D;

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and the...

We survey some classical norm inequalities of Hardy, Kallman, Kato, Kolmogorov, Landau, Littlewood, and Rota the type \[ \|A f\|_{\mathcal{X}}^2 \leq C \|f\|_{\mathcal{X}} \big\|A^2 f\big\|_{\mathcal{X}}, \quad f \in dom\big(A^2\big), \] recall that under exceedingly stronger hypotheses on operator $A$ and/or Banach space $\mathcal{X}$, optimal constant $C$ in these diminishes from $4$ (e.g., w...

We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n = 2) leads to a direct proof of Onofri inequality on S.

We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CRpluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequali...

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young's and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young's inequalities are promoted, the operator version and the Hilbert-Schmidt form ...