Related papers: Operator-valued dyadic BMO spaces

We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition…

We consider the dyadic paraproducts $\pi_\f$ on $\T$ associated with an $\M$-valued function $\f.$ Here $\T$ is the unit circle and $\M$ is a tracial von Neumann algebra. We prove that their boundedness on $L^p(\T,L^p(\M))$ for some…

Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[\pi_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $\pi_a$ is the $d$-adic martingale…

We address $L^p(\mu)\rightarrow L^p(\lambda)$ bounds for paraproducts in the Bloom setting. We introduce certain "sparse BMO" functions associated with sparse collections with no infinitely increasing chains, and use these to express sparse…

Denote by $M_n$ the algebra of $n\times n$ matrices. We consider the dyadic paraproducts $\pi_b$ associated with $M_n$ valued functions $b$, and show that the $L^\infty (M_n)$ norm of $b$ does not dominate $||\pi_b||_{L^2(\ell _n^2)\to…

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of…

It is shown that for $0<p,q,r<\infty$, with $\frac{1}{q} = \frac{1}{p} + \frac{1}{r}$, the operator norm of the dyadic paraproduct of the form \[ \pi_g(f) := \sum_{R \in \mathcal{D}\otimes\mathcal{D}} g_R \left\langle f \right\rangle_{R}…

Consider the second order divergence form elliptic operator $L$ with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calder\'{o}n-Zygmund theory.…

We investigate a scale of dyadic operator-valued BMO spaces, corresponding to the different yet equivalent characterizations of dyadic BMO in the scalar case. In the language of operator spaces, we investigate different operator space…

Let S be the semidirect product of R^d and R^+ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H^1 and a BMO space in this…

We give an explicit formula for one possible Bellman function associated with the $L^p$ boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings,…

Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $\mu$ satisfying the doubling property and let $\{\mathcal{A}_t\}_{t>0}$, be a generalized approximations to the identity, for example $\{\mathcal{A}_t\}$…

By $BMO_o(R)$ we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in $BMO_o(R)$ with bounded support as those ones that can be written as a sum of a…

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued…

Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \infty$, and $T$ be any of the Riesz transforms. We will characterize the boundedness of the commutator $[T, B]$ on $L^p(W)$ in terms of the…

We introduce multilinear analogues of dyadic paraproduct operators and Haar Multipliers, and study boundedness properties of these operators and their commutators. We also characterize dyadic BMO functions via the boundedness of certain…

This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of $BMO$-type spaces. The results are formulated in a very general framework in which $BMO$ spaces are…

The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, the boundedness of operator-valued singular integrals…

We discuss the dyadic John-Nirenberg space that is a generalization of functions of bounded mean oscillation. A John-Nirenberg inequality, which gives a weak type estimate for the oscillation of a function, is discussed in the setting of…

Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…