Abstract
We prove complex interpolation theorems for analytic families of multilinear operators defined on quasi-Banach spaces, with explicit constants on the intermediate spaces. We obtain analogous results for analytic families of operators defined on spaces generated by the Calderón method applied to couples of quasi-Banach lattices with nontrivial lattice convexity. As an application we derive a multilinear version of Stein’s classical interpolation theorem for analytic families of operators taking values in Lebesgue, Lorentz, and Hardy spaces. We use this theorem to prove that the bilinear Bochner–Riesz operator is bounded from Lp(Rn)×Lp(Rn) into Lp/2(Rn) for 1<p<2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.