References & Citations
Mathematics > Functional Analysis
Title: Bounds on the Phillips calculus of abstract first order differential operators
(Submitted on 18 Dec 2020 (v1), last revised 24 Aug 2021 (this version, v4))
Abstract: For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction of first order differential operators and prove similar spectral multiplier estimates assuming only that the group is bounded on $L^2$ rather than $L^p$. We also prove an R-bounded H\"ormander calculus result by assuming an abstract Sobolev embedding property and show that the square of a perturbed Hodge-Dirac operator has such calculus.
Submission history
From: Himani Sharma [view email][v1] Fri, 18 Dec 2020 03:59:56 GMT (19kb)
[v2] Mon, 4 Jan 2021 12:16:56 GMT (19kb)
[v3] Sat, 9 Jan 2021 04:34:35 GMT (19kb)
[v4] Tue, 24 Aug 2021 08:59:11 GMT (17kb)
Link back to: arXiv, form interface, contact.