BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality

2004 ◽  
Vol 249 (2) ◽  
pp. 329-356 ◽  
Author(s):  
J. Dziubański ◽  
G. Garrigós ◽  
T. Martínez ◽  
J. L. Torrea ◽  
J. Zienkiewicz
Keyword(s):  
Schrödinger Operators ◽  
Hölder Inequality ◽  
Schrodinger Operators ◽  
Reverse Hölder Inequality ◽  
Bmo Spaces ◽  
Reverse Hölder

RIESZ TRANSFORMS AND LITTLEWOOD–PALEY SQUARE FUNCTION ASSOCIATED TO SCHRÖDINGER OPERATORS ON NEW WEIGHTED SPACES

2018 ◽  
Vol 105 (2) ◽  
pp. 201-228
Author(s):  
NGUYEN NGOC TRONG ◽  
LE XUAN TRUONG
Keyword(s):  
Schrödinger Operators ◽  
Hölder Inequality ◽  
Riesz Transforms ◽  
Bounded Mean Oscillation ◽  
Schrodinger Operators ◽  
Square Function ◽  
Reverse Hölder Inequality ◽  
Lipschitz Spaces ◽  
Mean Oscillation ◽  
Reverse Hölder

Let ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+{\mathcal{V}}$ be a Schrödinger operator on $\mathbb{R}^{n},n\geq 3$, where ${\mathcal{V}}$ is a potential satisfying an appropriate reverse Hölder inequality. In this paper, we prove the boundedness of the Riesz transforms and the Littlewood–Paley square function associated with Schrödinger operators ${\mathcal{L}}$ in some new function spaces, such as new weighted Bounded Mean Oscillation (BMO) and weighted Lipschitz spaces, associated with ${\mathcal{L}}$. Our results extend certain well-known results.

Weighted BMO Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operator

2013 ◽  
Vol 303-306 ◽  
pp. 1613-1617
Author(s):  
Wen Hua Gao
Keyword(s):  
Schrödinger Operator ◽  
Hölder Inequality ◽  
Riesz Transforms ◽  
Schrodinger Operator ◽  
Reverse Hölder Inequality ◽  
Weighted Function ◽  
Bmo Function ◽  
Weighted Bmo ◽  
Bmo Spaces ◽  
Reverse Hölder

Schrödinger operator; Weighted BMO spaces; Reverse Hölder inequality; Commutator Abstract. In this paper, the Schrödinger operator on n dimensions Euclid space with the non-zero, nonnegative potential function satisfying the reverse Hölder inequality is considered. The weighted boundedness of the commutators composed of several Riesz transforms associated with the Schrödinger operator and weighted BMO function on weighted Lebesgue integral spaces are obtained, for some weighted function.

The reverse Hölder inequality for power means

2012 ◽  
Vol 183 (6) ◽  
pp. 762-771
Author(s):  
Viktor D. Didenko ◽  
Anatolii A. Korenovskyi
Keyword(s):  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Power Means ◽  
Reverse Hölder

scholarly journals Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators

2019 ◽  
Vol 68 (1) ◽  
pp. 247-289
Author(s):  
Jorge Betancor ◽  
Xuan Duong ◽  
Ji Li ◽  
Brent Wick ◽  
Dongyong Yang
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Bmo Spaces ◽  
Iterated Commutators

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$n>4$.

scholarly journals Torsional rigidity on compact Riemannian manifolds with lower Ricci curvature bounds

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Najoua Gamara ◽  
Abdelhalim Hasnaoui ◽  
Akrem Makni
Keyword(s):  
Riemannian Manifold ◽  
Dirichlet Problem ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Torsional Rigidity ◽  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Curvature Bounds ◽  
Reverse Hölder

AbstractIn this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds. We also prove an isoperimetric inequality for the torsional ridigity of such domains

scholarly journals Zeros for the Gradients of WeaklyA-Harmonic Tensors

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Yuxia Tong ◽  
Jiantao Gu ◽  
Shenzhou Zheng
Keyword(s):  
Regularity Property ◽  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Caccioppoli Inequality ◽  
Reverse Hölder ◽  
Weak Reverse Hölder Inequality ◽  
Weak Reverse Holder Inequality

The Caccioppoli inequality of weaklyA-harmonic tensors has been proved, which can be used to consider the weak reverse Hölder inequality, regularity property, and zeros of weaklyA-harmonic tensors.

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