A Remark on Littlewood-Paley projections
Younghun Hong
TL;DR
This paper derives kernel estimates for Littlewood-Paley projections linked to Schrödinger operators with short-range potentials in three dimensions, leading to proofs of homogeneous Sobolev inequalities.
Contribution
It provides new kernel estimates for Littlewood-Paley projections associated with Schrödinger operators with short-range potentials in D.
Findings
Kernel estimates for Littlewood-Paley projections established
Homogeneous Sobolev inequality proven as a corollary
Applicable to a large class of short-range potentials
Abstract
We establish the kernel estimates for the Littlewood-Paley projections associated with a Schr\"odinger operator H=-\Delta+V in \mathbb{R}^3 for a large class of short-range potentials V(x). As a corollary, we prove the homogeneous Sobolev inequality.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Advanced Harmonic Analysis Research