RT Journal Article
T1 Duality of mixed norm spaces induced by radial one-sided doubling weights
A1 Moreno, Álvaro Miguel
A1 Peláez-Márquez, José Ángel
K1 Bergman, Espacios de
AB For $0<p,q<\infty$ and $\omega$ a radial weight, the space $L^{p,q}_\omega$ consists of those complex-valued measurable functions $f$ on the unit disk such that		$$		\| f\|_{L^{p,q}_\omega}^q = \int_0^1 \left (\frac{1}{2\pi}\int_0^{2\pi}|f(re^{i\theta})|^pd\theta \right )^{\frac{q}{p}}r\omega(r)\,dr, 		$$		and the mixed norm space $A^{p,q}_\omega$ is the subset of $L^{p,q}_\omega$ consisting of analytic functions. \\		 We say that a radial weight $\omega$ belongs to $\widehat{\mathcal{D}}$ if there exists $C=C(\omega)>0$ such that $$\int_r^1\omega(s)ds \leq C \int_{\frac{1+r}{2}}^1\omega(s)\,ds, \quad 0\leq r <1.$$ We describe the dual space of $A^{p,q}_\omega$ for $0<p,q<\infty$ and  $\omega\in\widehat{\mathcal{D}}$. Later on, 		we  apply the obtained description of the dual space of $A^{p,q}_\omega$ to prove that the Bergman projection induced by $\omega$, $P_\omega$, is bounded on $L^{p,q}_\omega$ for $1<p,q<\infty$ and  $\omega\in \widehat{\mathcal{D}}$. Besides, if $\omega\in\DD$ and  $1<p,q<\infty$, we also prove that $P_\omega$ and the corresponding maximal Bergman projection $P_\omega^+$ are  simultaneously bounded on $L^{p,q}_\om$  if and only if  $\omega\in\mathcal{D}$.
PB Springer Nature
YR 2025
FD 2025-12-05
LK https://hdl.handle.net/10630/45343
UL https://hdl.handle.net/10630/45343
LA eng
NO Á.M. Moreno, J.Á. Peláez, Duality of Mixed Norm Spaces Induced by Radial One-Sided Doubling Weights, J. Geom. Anal. 36 (2026), no.~1, Paper No. 31
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 15 abr 2026