Banach Journal of Mathematical Analysis

Poisson semigroup, area function, and the characterization of Hardy space associated to degenerate Schrödinger operators

Jizheng Huang, Pengtao Li, and Yu Liu

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Abstract

Let

Lf(x)=1ω(x)i,ji(aij()jf)(x)+V(x)f(x) be the degenerate Schrödinger operator, where ω is a weight from the Muckenhoupt class A2 and V is a nonnegative potential that belongs to a certain reverse Hölder class with respect to the measure ω(x)dx. Based on some smoothness estimates of the Poisson semigroup etL, we introduce the area function SPL associated with etL to characterize the Hardy space associated with L.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 4 (2016), 727-749.

Dates
Received: 6 November 2015
Accepted: 6 January 2016
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1472657854

Digital Object Identifier
doi:10.1215/17358787-3649986

Mathematical Reviews number (MathSciNet)
MR3543909

Zentralblatt MATH identifier
1347.42037

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Hardy space Schrödinger operator atom area integral Poisson semigroup area function

Citation

Huang, Jizheng; Li, Pengtao; Liu, Yu. Poisson semigroup, area function, and the characterization of Hardy space associated to degenerate Schrödinger operators. Banach J. Math. Anal. 10 (2016), no. 4, 727--749. doi:10.1215/17358787-3649986. https://projecteuclid.org/euclid.bjma/1472657854


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