Related papers: Pointwise weighted approximation of functions with…

Let $\mathbb{R}=(-\infty,\infty)$, and let $Q\in C^1(\mathbb{R}): \mathbb{R}\rightarrow[0,\infty)$ be an even function. We consider the exponential weights $w(x)=e^{-Q(x)}$, $x\in \mathbb{R}$. In this paper we obtain a pointwise convergence…

We study the convergence of Bernstein type operators leading to two results. The first: The kernel $K_n$ of the Bernstein-Durrmeyer operator at each point $x \in (0, 1)$ $\unicode{x2013}$ that is $K_n(x, t) dt$ $\unicode{x2013}$ once…

Using Bellman function approach, we present new proofs of weighted $L^2$ inequalities for square functions, with the optimal dependence on the $A_2$ characteristics of the weight and further explicit constants. We study the estimates both…

We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…

Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spaces to weighted one-sided…

Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is…

We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…

Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i=0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is…

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner-Riesz multiplier at the critical index $B_{(n-1)/2}$.…

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…

We study sufficient conditions on weight functions under which norm approximations by analytic polynomials are possible. The weights we study include radial, non-radial, and angular weights.

A two-variable generalization of the Big $-1$ Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big $-1$ Jacobi polynomials. Their orthogonality measure is…

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…

We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$ and a scale of Hilbert function spaces in the unit $2$-ball having reproducing…

In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…

The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…

In the present work we characterized full operators and we showed some properties that have nonfull injectives operators. With the results developed for full operators, we affirmatively respond two questions formulated by Bravo and Feintuch…

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…

Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…