Related papers: Hankel Operators and Weak Factorization for Hardy-…

We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{\Phi_1} (\mathbb B^n)$ into $H^{\Phi_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?\Phi_1$…

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha(\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for…

In this work, we prove that the product of a function belonging to a Hardy-Orlicz space $H^{\Phi_{1}}$ and a function from another Hardy-Orlicz space $H^{\Phi_{2}}$ belongs to a third Hardy-Orlicz space $H^{\Phi_{3}}$. Moreover, we…

Let $\Omega$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (\Omega)$ with the Dirichlet boundary condition, and the…

Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orlicz-Hardy space $h^{\Phi}_{\omega}(\mathbb{R}^n)$…

Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $\varphi:\ \Omega\times[0,\infty)\to [0,\infty)$ be a Musielak--Orlicz function. In this article, the authors establish the atomic characterizations of weak martingale…

Let $\Omega$ be a bounded convex domain in $\mathbb{C}^{n}$, $n\geq 2$, $1\leq q\leq (n-1)$, and $\phi\in C(\bar{\Omega})$. If the Hankel operator $H^{q-1}_{\phi}$ on $(0,q-1)$--forms with symbol $\phi$ is compact, then $\phi$ is…

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz…

Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\infty)$ of upper type 1 and of strictly critical…

Let $\Omega$ be a bounded convex Reinhardt domain in $\mathbb{C}^2$ and $\phi\in C(\bar{\Omega})$. We show that the Hankel operator $H_{\phi}$ is compact if and only if $\phi$ is holomorphic along every non-trivial analytic disc in the…

We consider here Musielak-Orlicz Sobolev (MOS) spaces $W^{k,\Phi}(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^d$, $k\in\mathbb{N}$ and $\Phi$ is a Musielak-Orlicz function. The main outcomes consist of the results on density…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

Let $\Omega$ be a bounded convex domain in $\mathbb{C}^{n}$. We show that if $\varphi \in C^{1}(\overline{\Omega})$ is holomorphic along analytic varieties in $b\Omega$, then $H^{q}_{\varphi}$, the Hankel operator with symbol $\varphi$, is…

Let $\Omega\subset \mathbb{C}^2$ be a bounded pseudoconvex complete Reinhardt domain with a smooth boundary. We study the behavior of analytic structure in the boundary of $\Omega$ and obtain a compactness result for Hankel operators on the…

Let $L$ be a one-to-one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the weak Hardy space…

Let $\Omega$ be either $\mathbb{R}^n$ or a strongly Lipschitz domain of $\mathbb{R}^n$, and $\omega\in A_{\infty}(\mathbb{R}^n)$ (the class of Muckenhoupt weights). Let $L$ be a second order divergence form elliptic operator on $L^2…

In this article, we investigate the (big) Hankel operators $H_f$ on Hardy spaces of strongly pseudoconvex domains with smooth boundaries in $\mathbb{C}^n$. We also give a necessary and sufficient condition for boundedness of the Hankel…

For $0 \leq \alpha < n$ and $m \in \mathbb{N} \cap \left(1 - \frac{\alpha}{n}, +\infty \right)$, we consider certain fractional type operators $T_{\alpha, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < \alpha < n$,…

We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of weighted Hardy-Orlicz spaces, when the Orlicz function…

We study in this paper very badly approximable matrix functions on the unit circle $\T$, i.e., matrix functions $\Phi$ such that the zero function is a superoptimal approximation of $\Phi$. The purpose of this paper is to obtain a…