Document Type

Article

Publication Date

11-2010

Publication Title

Applied Mathematics

DOI

10.4236/am.2010.15056

ISSN

2152-7393

Abstract

Let H = -Δ+V be a Schrödinger operator on Rn. We show that gradient estimates for the heat kernel of H with upper Gaussian bounds imply polynomial decay for the kernels of certain smooth dyadic spectral operators. The latter decay property has been known to play an important role in the Littlewood-Paley theory for Lp and Sobolev spaces. We are able to establish the result by modifying Hebisch and the author’s recent proofs. We give a counterexample in one dimension to show that there exists V in the Schwartz class such that the long time gradient heat kernel estimate fails.

Comments

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