Related papers: Functional Calculus on BMO-type Spaces of Bourgain…

Via the new weight $A_{\vec p}^{\infty}(\varphi)$ and the new $BMO$ function, the authors introduce a new class of multilinear square operators $T$ with generalized kernels. The boundedness of multilinear commutators and multilinear…

A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…

We study mapping properties of Toeplitz operators $T_\mu$ associated to nonnegative Borel measure $\mu$ on the complex space $\mathbb{C}^n$. We, in particular, describe the bounded and compact operators $T_\mu$ acting between Fock spaces in…

In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch…

Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual…

Let $T(f)$ denote the Littlewood--Paley square operators, including the Littlewood--Paley $\mathcal{G}$-function $\mathcal{G}(f)$, Lusin's area integral $\mathcal{S}(f)$ and Stein's function $\mathcal{G}^{\ast}_{\lambda}(f)$ with…

We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$. We obtain several equivalent formulations of $\|\pi_B\|$ in terms of the norm of the…

For a Dirichlet series symbol $g(s) = \sum_{n \geq 1} b_n n^{-s}$, the associated Volterra operator $\mathbf{T}_g$ acting on a Dirichlet series $f(s)=\sum_{n\ge 1} a_n n^{-s}$ is defined by the integral $f\mapsto -\int_{s}^{+\infty}…

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 $\{\mathcal{A}_t\}$…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of…

A Bourgain--Brezis--Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in…

We deal with a reverse Carleson measure inequality for the tent spaces of analytic functions in the unit disc $\mathbb{D}$ of the complex plane. The tent spaces of measurable functions were introduced by Coifman, Meyer and Stein. Let $1\leq…

Let $(X,\mu)$ be a space of homogeneous type satisfying $\mu(X) =\infty$, the doubling property and the reverse doubling condition. Let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel enjoys a Gaussian upper bound.…

We look at Toeplitz operators $T_\nu$ on the Fock Space (also known as the Segal-Bargmann space) which have a positive Borel measure $\nu$ as a symbol. We characterize when $\left(T_\nu\right)^s$ for $0<s\leq 1$ is in the symmetrically…

In this paper, we study necessary and sufficient conditions for a positive Borel measure $\mu$ on the complex space $\mathbb{C}$ to be a $(\infty,q)$ or $(p,\infty)$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we…

We introduce the homogeneous (inhomogeneous) matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces and obtain their equivalent norms. We also obtain their characterizations by Peetre type maximal functions, Lusin-area function,…

Let $\L$ be a Schr\"odinger operator of the form $\L=-\Delta+V$ acting on $L^2(\mathbb R^n)$, $n\geq3$, where the nonnegative potential $V$ belongs to the reverse H\"older class $B_q$ for some $q\geq n.$ Let ${\rm BMO}_{{\mathcal{L}}}(\RR)$…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…

Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in…