Boundedness of dyadic paraproducts on matrix weighted LpL^p

In this paper, we show that dyadic paraproducts $\pi_b$ with $b$ in dyadic BMO are bounded on matrix weighted $L^p(W)$ if $W$ is a matrix $\text{A}_p$ weight.Comment: This paper has been withdrawn, and is vastly generalized by https://arxiv.org/abs/1507.0403

A Characterization of Norm Compactness in the Bochner Space Lp(G;B)L^p (G ; B) For an Arbitrary Locally Compact Group GG

In this paper, we generalize a result of N. Dinculeanu which characterizes norm compactness in the Bochner space $L^p(G ; B)$ in terms of an approximate identity and translation operators, where $G$ is a locally compact abelian group and $B$ is a Banach space. Our characterization includes the case where $G$ is nonabelian, and we weaken the hypotheses on the approximate identity used, providing new results even for the case $B = \mathbb{C}$ and $G = \mathbb{R}^n.$Comment: 13 pages, accepted into the "Journal of Mathematical Analysis and Applications.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0