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

This is an open access article retrieved from Applied Mathematics.

All articles from Applied Mathematics (AM) have "free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself."

Download

Share

COinS