The $L^p$ boundedness of the Bergman projection for a class of bounded Hartogs domains
By Liwei Chen. 2013
69 citations recorded by the source corpus.
We generalize the Hartogs triangle to a class of bounded Hartogs domains, and we prove that the corresponding Bergman projections are bounded on $L^p$ if and only if $p$ is in the range $(\frac{2n}{n+1},\frac{2n}{n-1})$.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/462ba4d2a8409483d7911f90a17ea5fcbde441b4
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In Applied Mathematics
Citations in the corpus
- mapping properties of the Bergman projection on the Hartogs triangle (2014, background): “.1 we can recover the following folk result: Corollary 1.1. (a) If 4 3 < p < 4, then BH is bounded (and surjective) from Lp(H) to Ap(H). (b) If p ≥ 4, then BH does not map Lp(H) into Ap(H). See [Che13] for a generalization of part (a) to a class of domains closely related to H. Note that for 2”
- The Bergman projection on fat Hartogs triangles: L^p boundedness (2015, background): “f k>1, while the Bergman kernel of D× D∗ is known to be zero-free. Thus, to prove Theorem 1.2 we must directly address the Bergman projection on Ωk, rather than transfer to D×D∗ as done in [2] and [3]. There is a general, though technical, point in our proofs below that seems worth noting. Once t”
- Bergman Subspaces and Subkernels: Degenerate $$L^p$$Lp Mapping and Zeroes (2016, result): “ively estimate these twodimensional integrals. BERGMAN SUBSPACES 11 The essential estimate below (without |w|−β in the integrand) has been re-discovered many times, see for instance [13], [24], [27], [8]. The proofs in these sources use well-known, but non-trivial, asymptotic results to derive the e”