相关论文: A new two weight estimates for a vector-valued pos…
We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.
We prove that an injective, not necessarily bounded weighted bilateral shift operator on $\ell^2(\mathbb{Z})$ is similar to a normal operator if and only if it is similar to a scalar multiple of the simple (i.e. unweighted) bilateral shift…
In this note, we find a new way to prove several properties of 2-alternating capacities.
The purpose of this paper is to describe a unified approach to proving vector-valued inequalities without relying on the full strength of weighted theory. Our applications include the Fefferman-Stein and Cordoba-Fefferman inequalities, as…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding…
We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a…
We propose a harmonic superspace description of the non-linear vector-tensor N=2 multiplet. We show that there exist two inequivalent version: the old one in which one of the vectors is the field-strength of a gauge two-form, and a new one…
We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal…
Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular…
Let $H$ be the Hardy operator and $I$ the identity operator acting on functions on the real half-line. We find optimal bounds for the operator $H - I$ in the setting of power weights and the cases of positive decreasing functions, positive…
Every diagonalmatrix D yields an endomorphism on the n-dimensional complex vectorspace. If one provides this space with Hoelder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
Sharp weighted estimates are obtained for vector-valued extensions of the Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators and Coifman-Rochberg-Weiss commutator. Those estimates will rely upon suitable pointwise estimates in…
New Hardy and Sobolev type inequalities involving $L^1$-norms of scalar and vector-valued functions in $\Bbb{R}^n$ are obtained. The work is related to some problems stated in the recent paper by Bourgain and Brezis
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two…
In this article, we investigate the ball version of von Neumann inequality for the class of doubly contractive $d$-tuple of weighted shift. We show that if the weighted shift is balanced or satisfies an appropriate weight condition, then it…
Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.
We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…
Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…