Related papers: Several generalized Bohr-type inequalities with tw…
We provide an explicit technical framework for proving very general two-weight commutator estimates in arbitrary parameters. The aim is to both clarify existing literature, which often explicitly focuses on two parameters only, and to…
We give necessary and sufficient conditions for two weight norm inequalities for Haar multipliers operators and for square functions. We also give sufficient conditions for two weight norm inequalities for the Hilbert transform.
We prove that the Bohr' radius for large functions is $e^{-\pi }.$
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \begin{align*} \bigg\| \,\int_{B(0,\cdot)} f \cdot \int_{B(0,\cdot)} g \,\bigg\|_{q,u,(0,\infty)} & \leq C \, \|f\|_{p_1,v_1,{\mathbb R}^n}…
We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…
The main goal of this paper is to generalize Bohr's phenomenon from complex one-dimensional analysis to higher dimensions in the framework of Quaternionic Analysis.
The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.
We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…
The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
In the paper, some lower bounds for polygamma functions are refined.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other "well localized" operators.
Several families of sharp Bernstein inequalities are established on the weighted $L^2$ space over parabolic domains, which include bounded or unbounded rotational paraboloids and parabolic surfaces. The main tool is a second-order…
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions…
There are a number of articles which deal with Bohr's phenomenon whereas only a few papers appeared in the literature on Rogosinski's radii for analytic functions defined on the unit disk $|z|<1$. In this article, we introduce and…