Littlewood-Paley Theorem for Schrödinger Operators

Authors

Shijun Zheng, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

12-2006

Publication Title

Analysis in Theory and Applications

DOI

10.1007/s10496-006-0353-1

ISSN

1573-8175

Abstract

Let H be a Schrödinger operator on ℝⁿ. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of L_p spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.

Recommended Citation

Zheng, Shijun. 2006. "Littlewood-Paley Theorem for Schrödinger Operators." Analysis in Theory and Applications, 22 (4): 353-361. doi: 10.1007/s10496-006-0353-1
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/695