Weighted Bergman spaces induced by rapidly increasing weights - Pelaez, Jose Angel (Memoirs of the American Mathematical Society, 2013)
This monograph is devoted to the study of the weighted Bergman space $A^p_ω$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $ω$ satisfying $\lim_{r→ 1^-}\frac{\int_r^1ω(s)\,ds}{ω(r)(1-r)}=∞.$ Every such $A^p_ω$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_α$. Even if it is well known that $H^p$ is the limit of $A^p_α$, as $α→-1$, in many respects, it is shown that $A^p_ω$ lies ``closer'' to $H^p$ than any $A^p_α$, and that several finer function-theoretic properties of $A^p_α$ do not carry over to $A^p_ω$.