The Kato Square Root Problem for Divergence Form Operators with Potential

Abstract

for all u ∈ D(|V | −) and some α ∈ (1, 2]. The class of potentials that will satisfy such a condition is known to contain the reverse Hölder class R H 2 and L n 2 (R n) in dimension n > 4. To prove the Kato estimate with potential, a non-homogeneous version of the framework introduced by Axelsson, Keith and McIntosh for proving quadratic estimates is developed. In addition to applying this non-homogeneous framework to the scalar Kato problem with zero-order potential, it will also be applied to the Kato problem for systems of equations with zero-order potential.

Non-Autonomous Maximal Regularity Under Besov Regularity in Time

“…)u ∈ L 2 (R n )}. Note that the estimate (3.2) is satisfied here (see [9][Theorem 1.2]). Next we assume that t → m(t, .…”

Schrödinger Operators and the Kato Square Root Problem

“…This class includes any potential V with range contained in some sector of angle ω V ∈ [0, π/2) and for which |V| belongs either to the reverse Hölder class RH 2 in any dimension or L n/2 (R n ) for n > 4. Some of this work has appeared in [4].…”