Boundedness of the Bergman projection on $L^p$ spaces with exponential weights
By O. Constantin, J. A. Pel'aez. 2013
47 citations recorded by the source corpus.
Let $v(r)=\exp\left(-\frac{\alpha}{1-r}\right)$ with $\alpha>0$, and let $\mathbb{D}$ be the unit disc in the complex plane. Denote by $A^p_v$ the subspace of analytic functions of $L^p(\mathbb{D},v)$ and let $P_v$ be the orthogonal projection from $L^2(\mathbb{D},v)$ onto $A^2_v$. In 2004, Dostanic revealed the intriguing fact that $P_v$ is bounded from $L^p(\mathbb{D},v)$ to $A^p_v$ only for $p=2$, and he posed the related problem of identifying the duals of $A^p_v$ for $p\ge 1$, $p\neq 2$. In this paper we propose a solution to this problem by proving that $P_v$ is bounded from $\,L^p(\D,v^{p/2})$ to $A^p_{v^{p/2}}$ whenever $1\le p <\infty$, and, consequently, the dual of $A^p_{v^{p/2}}$ for $p\ge 1$ can be identified with $A^{q}_{v^{q/2}}$, where $1/p+1/q=1$. In addition, we also address a similar question on some classes of weighted Fock spaces.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/ff2d9d27c7a5f152ca676001434c0ec16b5233c7
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In Algebra and Number Theory
In Applied Mathematics
Citations in the corpus
- Two weight inequality for Bergman projection (2014, background): “ plays a role when Ap ωis sufficiently close to the Hardy space Hp. It is worth mentioning that Pωfails to be bounded on L p ωif ωdecreases sufficiently fast (at least exponentially) and is smooth enough [8, 9, 10, 21]. In fact, as far as we know, to characterize those radial weights for which Pω : L p ”
- Small weighted Bergman spaces (2015, background): “ϕ, where ∆ϕ>0, and considering the disc D z,√ c ∆ϕ(z) . The weighted Bergman spaces Ap ω induced by rapidly decreasing weights are similar, but not identical, to weighted Fock spaces [44]. See [9, 8, 22, 23, 45, 46, 58] for progress on the theory of these spaces. For further information on any ”