scholarly journals Weighted and vector-valued variational estimates for ergodic averages

2016 ◽  
Vol 38 (1) ◽  
pp. 244-256 ◽  
Author(s):  
BEN KRAUSE ◽  
PAVEL ZORIN-KRANICH
Keyword(s):  
Hölder Inequality ◽  
Square Function ◽  
Reverse Hölder Inequality ◽  
Ergodic Averages ◽  
Function Estimate ◽  
Reverse Hölder ◽  
Vector Valued

We prove weighted and vector-valued variational estimates for ergodic averages on$\mathbb{R}^{d}$. The weighted square function estimate relating ergodic averages to the dyadic martingale is obtained using an$\ell ^{r}$version of a reverse Hölder inequality for variation seminorms.

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.

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 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.

scholarly journals End Point Estimate of Littlewood-Paley Operator Associated to the Generalized Schrödinger Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yanping Chen ◽  
Wenyu Tao
Keyword(s):  
Schrödinger Operator ◽  
Radon Measure ◽  
Hölder Inequality ◽  
Point Estimate ◽  
Schrodinger Operator ◽  
Reverse Hölder Inequality ◽  
Scale Invariant ◽  
End Point ◽  
Reverse Hölder ◽  
Generalized Schrödinger Operator

Let L = − Δ + μ be the generalized Schrödinger operator on ℝ d , d ≥ 3 , where μ ≠ 0 is a nonnegative Radon measure satisfying certain scale-invariant Kato conditions and doubling conditions. In this work, we give a new BMO space associated to the generalized Schrödinger operator L , BM O θ , L , which is bigger than the BMO spaces related to the classical Schrödinger operators A = − Δ + V , with V a potential satisfying a reverse Hölder inequality introduced by Dziubański et al. in 2005. Besides, the boundedness of the Littlewood-Paley operators associated to L in BM O θ , L also be proved.

SOME REVERSE DYNAMIC INEQUALITIES ON TIME SCALES

2017 ◽  
Vol 96 (3) ◽  
pp. 445-454 ◽  
Author(s):  
R. P. AGARWAL ◽  
R. R. MAHMOUD ◽  
D. O’REGAN ◽  
S. H. SAKER
Keyword(s):  
Time Scales ◽  
Hölder Inequality ◽  
Chain Rule ◽  
Fubini Theorem ◽  
Reverse Hölder Inequality ◽  
Reverse Hölder

In this paper, we prove some new reverse dynamic inequalities of Renaud- and Bennett-type on time scales. The results are established using the time scales Fubini theorem, the reverse Hölder inequality and a time scales chain rule.

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