scholarly journals Hardy Spaces Associated to Schrödinger Operators on Product Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Liang Song ◽  
Chaoqiang Tan
Keyword(s):  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Schrödinger Operators ◽  
Nonnegative Function ◽  
Maximal Functions ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Product Spaces ◽  
Area Integral ◽  
Lusin Area Integral

LetL=−Δ+Vbe a Schrödinger operator onℝn, whereV∈Lloc1(ℝn)is a nonnegative function onℝn. In this article, we show that the Hardy spacesLon product spaces can be characterized in terms of the Lusin area integral, atomic decomposition, and maximal functions.

scholarly journals AN ATOMIC DECOMPOSITION FOR HARDY SPACES ASSOCIATED TO SCHRÖDINGER OPERATORS

2011 ◽  
Vol 91 (1) ◽  
pp. 125-144 ◽  
Author(s):  
LIANG SONG ◽  
CHAOQIANG TAN ◽  
LIXIN YAN
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Schrödinger Operators ◽  
Nonnegative Function ◽  
Schrodinger Operators ◽  
Integrable Functions ◽  
Function Characterization ◽  
Product Domains

AbstractLetL=−Δ+Vbe a Schrödinger operator on ℝnwhereVis a nonnegative function in the spaceL1loc(ℝn) of locally integrable functions on ℝn. In this paper we provide an atomic decomposition for the Hardy spaceH1L(ℝn) associated toLin terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy spaceH1L(ℝn×ℝn) on product domains.

scholarly journals Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hua Zhu
Keyword(s):  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Critical Radius ◽  
Schrödinger Operators ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Local Hardy Spaces ◽  
Radius Function

We characterize the weighted weak local Hardy spacesWhρp(ω)related to the critical radius functionρand weightsω∈A∞ρ,∞(Rn)which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.

Coincidence of weighted Hardy spaces associated with higher-order Schrödinger operators

2021 ◽  
pp. 103031
Author(s):  
Trong Ngoc Nguyen ◽  
Truong Xuan Le ◽  
Tan Duc Do
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Weighted Hardy Spaces

Real-variable characterizations of Musielak-Orlicz-Hardy spaces associated with Schrödinger operators on domains

2015 ◽  
Vol 39 (3) ◽  
pp. 533-569 ◽  
Author(s):  
Der-Chen Chang ◽  
Zunwei Fu ◽  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Real Variable ◽  
Schrodinger Operators

scholarly journals Spectral characterization and Schrödinger operator of space-like submanifolds

2015 ◽  
Vol 23 (2) ◽  
pp. 241-257
Author(s):  
Shichang Shu ◽  
Tianmin Zhu
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Spectral Characterization ◽  
Schrodinger Operators ◽  
First Eigenvalue ◽  
Schrodinger Operator ◽  
De Sitter ◽  
Totally Umbilical ◽  
The First Eigenvalue ◽  
Spectral Characterizations

Abstract In this paper, we would like to study space-like submanifolds in a de Sitter spaces Spn+p(1). We define and discuss three Schrödinger operators LH, LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH, LR and LR/H respectively.

Estimates for second-order Riesz transforms associated with magnetic Schrödinger operators on Musielak-Orlicz-Hardy spaces

2014 ◽  
Vol 93 (11) ◽  
pp. 2519-2545 ◽  
Author(s):  
Jun Cao ◽  
Der-Chen Chang ◽  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Second Order ◽  
Riesz Transforms ◽  
Schrodinger Operators

scholarly journals Counterexamples to the Kotani–Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces

2016 ◽  
Vol 293 ◽  
pp. 738-781 ◽  
Author(s):  
David Damanik ◽  
Peter Yuditskii
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals Hardy spaces for Bessel-Schrödinger operators

2018 ◽  
Vol 291 (5-6) ◽  
pp. 908-927
Author(s):  
Edyta Kania ◽  
Marcin Preisner
Keyword(s):  
Hardy Spaces ◽  
Schrödinger Operators ◽  
Schrodinger Operators

THE ESTIMATES OF RIESZ TRANSFORMS ASSOCIATED TO SCHRÖDINGER OPERATORS

2016 ◽  
Vol 101 (3) ◽  
pp. 290-309 ◽  
Author(s):  
QINGQUAN DENG ◽  
YONG DING ◽  
XIAOHUA YAO
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Riesz Transform ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Reverse Hölder Class ◽  
Holder Class ◽  
Small Norm ◽  
Reverse Hölder

Let$H=-\unicode[STIX]{x1D6E5}+V$be a Schrödinger operator with some general signed potential$V$. This paper is mainly devoted to establishing the$L^{q}$-boundedness of the Riesz transform$\unicode[STIX]{x1D6FB}H^{-1/2}$for$q>2$. We mainly prove that under certain conditions on$V$, the Riesz transform$\unicode[STIX]{x1D6FB}H^{-1/2}$is bounded on$L^{q}$for all$q\in [2,p_{0})$with a given$2<p_{0}<n$. As an application, the main result can be applied to the operator$H=-\unicode[STIX]{x1D6E5}+V_{+}-V_{-}$, where$V_{+}$belongs to the reverse Hölder class$B_{\unicode[STIX]{x1D703}}$and$V_{-}\in L^{n/2,\infty }$with a small norm. In particular, if$V_{-}=-\unicode[STIX]{x1D6FE}|x|^{-2}$for some positive number$\unicode[STIX]{x1D6FE}$,$\unicode[STIX]{x1D6FB}H^{-1/2}$is bounded on$L^{q}$for all$q\in [2,n/2)$and$n>4$.

Does Each Symmetric Operator Have a Stability Domain?

1998 ◽  
Vol 10 (06) ◽  
pp. 829-850 ◽  
Author(s):  
H. Neidhardt ◽  
V. A. Zagrebnov
Keyword(s):  
Symmetric Operator ◽  
Schrödinger Operators ◽  
Stability Domain ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Center Problem ◽  
Abstract Result ◽  
Perturbed System ◽  
Regularization Problem ◽  
Ill Posed

We show that any symmetric operator H has a dense maximal b-stability domain [Formula: see text] (i.e. [Formula: see text], b∈R1) if and only if H is unbounded from above. This abstract result allows an application to singular perturbed Schrödinger operators which are not semi-bounded from below, i.e., to the so-called "fall to the center problem". It turns out that in this case the regularization problem is always ill-posed which implies that there is no unique "right Hamiltonian" for corresponding perturbed system. We give an example of singular perturbed Schrödinger operator for which stability domains are described explicitly.

Sign in / Sign up

Export Citation Format

Share Document