由径向权重诱导的伯克曼投影作用于增长空间
复变函数
2024-06-27 v1
摘要
设 ω \omega ω D \mathbb{D} D ω x = ∫ 0 1 s x ω ( s ) d s \omega_x =\int_0^1 s^x \omega(s)\,ds ω x = ∫ 0 1 s x ω ( s ) d s x ≥ 0 x\ge 0 x ≥ 0 ω \omega ω ω ^ ( r ) = ∫ r 1 ω ( s ) d s \widehat{\omega}(r)=\int_r^1 \omega(s)\,ds ω ( r ) = ∫ r 1 ω ( s ) d s ω \omega ω sup 0 < r < 1 ω ^ ( r ) ω ^ ( 1 + r 2 ) < ∞ , \sup_{0<r<1}\frac{\widehat{\omega}(r)}{\widehat{\omega}\left(\frac{1+r}{2}\right)}<\infty, 0 < r < 1 sup ω ( 2 1 + r ) ω ( r ) < ∞ , ω \omega ω D ^ \widehat{\mathcal{D}} D ν \nu ν ω \omega ω D ^ \widehat{\mathcal{D}} D ω \omega ω ν \nu ν ω \omega ω P ω P_\omega P ω L ν ^ ∞ = { f : ∥ f ∥ ∞ , v = e s s s u p z ∈ D ∣ f ( z ) ∣ ν ^ ( z ) < ∞ } L^\infty_{\widehat{\nu}} =\{ f: \|f\|_{\infty,v}={ esssup}_{z\in\mathbb{D}} |f(z)|\widehat{\nu}(z)<\infty\} L ν ∞ = { f : ∥ f ∥ ∞ , v = esss u p z ∈ D ∣ f ( z ) ∣ ν ( z ) < ∞ } P ω P_\omega P ω L ν ^ ∞ L^\infty_{\widehat{\nu}} L ν ∞ sup z ∈ D ( 1 − ∣ z ∣ ) ν ^ ( z ) ∣ f ′ ( z ) ∣ < ∞ \sup_{z\in \mathbb{D}}(1-|z|)\widehat{\nu}(z) |f'(z)|<\infty sup z ∈ D ( 1 − ∣ z ∣ ) ν ( z ) ∣ f ′ ( z ) ∣ < ∞ B ν ^ ∞ B^\infty_{\widehat{\nu}} B ν ∞
引用
@article{arxiv.2406.18446,
title = {Bergman projection induced by radial weight acting on growth spaces},
author = {Álvaro Miguel Moreno and José Ángel Peláez and Jari Taskinen},
journal= {arXiv preprint arXiv:2406.18446},
year = {2024}
}