Two weight inequality for Bergman projection
By J. A. Pel'aez, Jouni Rattya. 2014
91 citations recorded by the source corpus.
The motivation of this paper comes from the two weight inequality $$\|P_\omega(f)\|_{L^p_v}\le C\|f\|_{L^p_v},\quad f\in L^p_v,$$ for the Bergman projection $P_\omega$ in the unit disc. We show that the boundedness of $P_\omega$ on $L^p_v$ is characterized in terms of self-improving Muckenhoupt and Bekoll\'e-Bonami type conditions when the radial weights $v$ and $\omega$ admit certain smoothness. En route to the proof we describe the asymptotic behavior of the $L^p$-means and the $L^p_v$-integrability of the reproducing kernels of the weighted Bergman space $A^2_\omega$.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d34818dbeb613431fcbd7ea87586e0597c735512
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Trace class criteria for Toeplitz and composition operators on small Bergman spaces (2014, methodology): “own that for such ω, many finer function theoretic properties of Ap ω are very different from those of A p α and, in particular, its harmonic analysis is similar to that of Hardy spaces in many aspects [17, 18, 19]. For any ω ∈ Db, the norm convergence in A2 ω implies the uniform convergence on compac”
- Bergman projection induced by radial weight. (2019, unknown): “Moreover, the main result in [25] characterizes (1.”