由径向单边倍权诱导的混合范数空间的对偶性
复变函数
2025-09-10 v1 泛函分析
摘要
对于 0 < p , q < ∞ 0<p,q<\infty 0 < p , q < ∞ ω \omega ω L ω p , q L^{p,q}_\omega L ω p , q ∥ f ∥ L ω p , q q = ∫ 0 1 ( 1 2 π ∫ 0 2 π ∣ f ( r e i θ ) ∣ p d θ ) q p r ω ( r ) d r , \| f\|_{L^{p,q}_\omega}^q = \int_0^1 \left (\frac{1}{2\pi}\int_0^{2\pi}|f(re^{i\theta})|^pd\theta \right )^{\frac{q}{p}}r\omega(r)\,dr, ∥ f ∥ L ω p , q q = ∫ 0 1 ( 2 π 1 ∫ 0 2 π ∣ f ( r e i θ ) ∣ p d θ ) p q r ω ( r ) d r , f f f A ω p , q A^{p,q}_\omega A ω p , q L ω p , q L^{p,q}_\omega L ω p , q ω \omega ω D ^ \widehat{\mathcal{D}} D C = C ( ω ) > 0 C=C(\omega)>0 C = C ( ω ) > 0 ∫ r 1 ω ( s ) d s ≤ C ∫ 1 + r 2 1 ω ( s ) d s 对每一个 0 ≤ r < 1. \int_r^1\omega(s)ds \leq C \int_{\frac{1+r}{2}}^1\omega(s)\,ds \,\, \text{对每一个}\,\, 0\leq r <1. ∫ r 1 ω ( s ) d s ≤ C ∫ 2 1 + r 1 ω ( s ) d s 对每一个 0 ≤ r < 1. 0 < p , q < ∞ 0<p,q<\infty 0 < p , q < ∞ ω ∈ D ^ \omega\in\widehat{\mathcal{D}} ω ∈ D A ω p , q A^{p,q}_\omega A ω p , q A ω p , q A^{p,q}_\omega A ω p , q ω \omega ω P ω P_\omega P ω 1 < p , q < ∞ 1<p,q<\infty 1 < p , q < ∞ ω ∈ D ^ \omega\in \widehat{\mathcal{D}} ω ∈ D L ω p , q L^{p,q}_\omega L ω p , q P ω P_\omega P ω P ω + P_\omega^+ P ω + 1 < p , q < ∞ 1<p,q<\infty 1 < p , q < ∞ ω ∈ D ^ \omega\in \widehat{\mathcal{D}} ω ∈ D L ω p , q L^{p,q}_\omega L ω p , q
引用
@article{arxiv.2509.07536,
title = {Duality of mixed norm spaces induced by radial one-sided doubling weight},
author = {Álvaro Miguel Moreno and José Ángel Peláez},
journal= {arXiv preprint arXiv:2509.07536},
year = {2025}
}