Year: 2024
Type: article
Abstract: Let $$\omega $$ ω be a radial weight on the unit disc of the complex plane $$\mathbb {D}$$ D and denote by $$\widehat{\omega }(r)=\int _r^1 \omega (s)\,ds$$ ω ^ ( r ) = ∫ r 1 ω ( s ) d s the tail integrals. A radial weight $$\omega $$ ω belongs to the class $$\widehat{\mathcal {D}}$$ D ^ if satisfies the upper doubling condition $$\begin{aligned} \sup _{0 sup 0 < r < 1 ω ^ ( r ) ω ^ 1 + r 2 < ∞ . If $$\nu $$ ν or $$\omega $$ ω belongs to $$\widehat{\mathcal {D}}$$ D ^ , we describe the boundedness of the Bergman projection $$P_\omega $$ P ω induced by $$\omega $$ ω on the growth space $$L^\infty _{\widehat{\nu }} =\{ f: \Vert f\Vert _{\infty ,v}=\text {ess sup}_{z\in \mathbb {D}} |f(z)|\widehat{\nu }(z)<\infty \}$$ L ν ^ ∞ = { f : ‖ f ‖ ∞ , v = ess sup z ∈ D | f ( z ) | ν ^ ( z
Institutions: Universidad de Málaga, University of Helsinki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4403734692