Two classes of integral operators over the Siegel upper half-space
We determine exactly when two classes of integral operators are bounded on weighted $L^p$ spaces over the Siegel upper half-space.
math.CV↗
arXiv subjects
Pengyan Hu
Publications and source records attributed to Pengyan Hu.
$L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space
We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.
math.CV↗
Weighted Composition Operators Acting on Harmonic Hardy Spaces
Suppose $n\geq 3$ and let $B$ be the open unit ball in $\mathbb{R}^n$. Let $φ: B\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $ψ$ be a $C^2$ function on $B$. We characterize bounded weighted composition operators $W_{φ,ψ}$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{φ,ψ}$ on $h^p(B)$ when $φ$ is a Möbius transformation of $B$.
math.CV↗