Littlewood-Paley theorem for Schrödinger operators

Shijun Zheng

doi:10.1007/s10496-006-0353-1

Littlewood-Paley theorem for Schrödinger operators

Shijun Zheng

Mathematical Sciences

University of South Carolina

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	353-361
Number of pages	9
Journal	Analysis in Theory and Applications
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s10496-006-0353-1
State	Published - Dec 2006

Scopus Subject Areas

Analysis
Applied Mathematics

Keywords

Functional calculus
Littlewood-Paley theory
Schrödinger operator

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10.1007/s10496-006-0353-1

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abstract = "Let H be a Schr{\"o}dinger 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 Lp 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.",

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AU - Zheng, Shijun

PY - 2006/12

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N2 - 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 Lp 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.

AB - 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 Lp 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.

KW - Functional calculus

KW - Littlewood-Paley theory

KW - Schrödinger operator

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U2 - 10.1007/s10496-006-0353-1

DO - 10.1007/s10496-006-0353-1

M3 - Article

SN - 1672-4070

VL - 22

SP - 353

EP - 361

JO - Analysis in Theory and Applications

JF - Analysis in Theory and Applications

IS - 4

ER -

Littlewood-Paley theorem for Schrödinger operators

Abstract

Scopus Subject Areas

Keywords

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