Photo by kellysikkema from unsplash
In this paper, we obtain the exact norm of the following integral operator $$P^{\alpha }_{t}$$Ptα$$\begin{aligned} P^{\alpha }_{t}f(z)=\int _{\mathbb {B}_{n}}\frac{f(w)}{(1- \langle z,w \rangle )^{n+t+\alpha }}dv_{t}(w),\ \alpha>0,\ t>-1, \end{aligned}$$Ptαf(z)=∫Bnf(w)(1-⟨z,w⟩)n+t+αdvt(w),α>0,t>-1,from $$L^{\infty }(\mathbb {B}_{n})$$L∞(Bn)… Click to show full abstract
In this paper, we obtain the exact norm of the following integral operator $$P^{\alpha }_{t}$$Ptα$$\begin{aligned} P^{\alpha }_{t}f(z)=\int _{\mathbb {B}_{n}}\frac{f(w)}{(1- \langle z,w \rangle )^{n+t+\alpha }}dv_{t}(w),\ \alpha>0,\ t>-1, \end{aligned}$$Ptαf(z)=∫Bnf(w)(1-⟨z,w⟩)n+t+αdvt(w),α>0,t>-1,from $$L^{\infty }(\mathbb {B}_{n})$$L∞(Bn) onto Bloch-type spaces $$\mathcal {B}_\alpha $$Bα over the unit ball $$\mathbb {B}_{n}$$Bn, which can be regarded as an another extension of the classical Bergman projection.
Journal Title: Complex Analysis and Operator Theory
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!