Boundary multipliers of a family of Mobius invariant function spaces

For $1<p<infty$ and $0<s<1$, let $mathcal{Q}^p_ s (mathbb{T})$ be the space of those functions $f$ which belong to $ L^p(mathbb{T})$ and satisfy [ sup_{Isubset mathbb{T}}frac{1}{|I|^s}int_Iint_Ifrac{|f(zeta)-f(eta)|^p}{|zeta-eta|^{2-s}}|dzeta||deta|<infty, ] where $|I|$ is the length of an arc $I$ of the unit circle $mathbb{T}$ . In this paper, we give a complete description of multipliers between $mathcal{Q}^p_ s (mathbb{T})$ spaces. The spectra of multiplication operators on $mathcal{Q}^p_ s (mathbb{T})$ are also obtained.

Characterization of Schatten class Hankel operators on weighted Bergman spaces

We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<infty$ of the Hankel operators $H_ f$ and $H_{bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.

Schatten class Toeplitz operators acting on large weighted Bergman spaces

A full description of the membership in the Schatten ideal $S_ p(A^2_{omega})$ for $0<p<infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.

Closure of Hardy spaces in the Bloch space

A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $Cn$ for $0<p<infty$ is given. When $0<pleq1$, the result is new even in the case of the unit disk.