On the Uniqueness of Maximal Functions

1996 ◽  
Vol 3 (1) ◽  
pp. 49-52
Author(s):  
L. Ephremidze
Keyword(s):  
Uniqueness Theorem ◽  
Maximal Operator ◽  
Maximal Functions ◽  
The One ◽  
The Uniqueness Theorem

Abstract The uniqueness theorem for the one-sided maximal operator has been proved.

Endpoint Regularity of Multisublinear Fractional Maximal Functions

2017 ◽  
Vol 60 (3) ◽  
pp. 586-603 ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Maximal Operators ◽  
One Dimensional ◽  
Regularity Properties ◽  
The One ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractIn this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy–Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on the vector-valued function with all ƒ j being BV-functions.

Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator

1994 ◽  
Vol 46 (5) ◽  
pp. 1057-1072 ◽  
Author(s):  
P. Ortega Salvador
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Measure Space ◽  
Maximal Functions ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
Measure Preserving Transformation ◽  
The One ◽  
Image Position ◽  
Lorentz Norm

AbstractIn this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal functionSimilar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.

scholarly journals On the lack of dimension-free estimates in Lp for maximal functions associated to radial measures

2010 ◽  
Vol 140 (3) ◽  
pp. 541-552 ◽  
Author(s):  
Alberto Criado
Keyword(s):  
Gaussian Measure ◽  
Maximal Operator ◽  
Recent Article ◽  
Maximal Functions

In a recent article Aldaz proved that the weak L1 bounds for the centred maximal operator associated to finite radial measures cannot be taken independently with respect to the dimension. We show that the same result holds for the Lp bounds of such measures with decreasing densities, at least for small p near to one. We also give some concrete examples, including the Gaussian measure, where better estimates with respect to the general case are obtained.

On the regularity of one-sided fractional maximal functions

2018 ◽  
Vol 68 (5) ◽  
pp. 1097-1112 ◽  
Author(s):  
Feng Liu
Keyword(s):  
Bounded Variation ◽  
Maximal Functions ◽  
Continuous Case ◽  
Discrete Case ◽  
Maximal Operators ◽  
Functions Of Bounded Variation ◽  
Sharp Bounds ◽  
Regularity Properties ◽  
Natural Extensions ◽  
The One

Abstract In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators $ \mathcal{M}_{\beta}^{+} $ and $ \mathcal{M}_{\beta}^{-} $ map $ W^{1,p}(\mathbb{R}) $ into $ W^{1,q}(\mathbb{R}) $ with 1 <p <∞, 0≤β<1/p and q=p/(1-pβ), boundedly and continuously. In addition, we also obtain the sharp bounds and continuity for the discrete one-sided fractional maximal operators $ M_{\beta}^{+} $ and $ M_{\beta}^{-} $ from $ \ell^{1}(\mathbb{Z}) $ to $ {\rm BV}(\mathbb{Z}) $. Here $ {\rm BV}(\mathbb{Z}) $ denotes the set of all functions of bounded variation defined on ℤ. The results we obtained represent significant and natural extensions of what was known previously.

scholarly journals The uniqueness theorem for entanglement measures

2002 ◽  
Vol 43 (9) ◽  
pp. 4252-4272 ◽  
Author(s):  
Matthew J. Donald ◽  
Michał Horodecki ◽  
Oliver Rudolph
Keyword(s):  
Uniqueness Theorem ◽  
Entanglement Measures ◽  
The Uniqueness Theorem

scholarly journals On the uniqueness theorem

1970 ◽  
Vol 14 (3) ◽  
pp. 376-384 ◽  
Author(s):  
Helmut Bender
Keyword(s):  
Uniqueness Theorem ◽  
The Uniqueness Theorem

scholarly journals Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Special Linear ◽  
Uncertain Variables ◽  
Important Theorem ◽  
Special Case ◽  
The Uniqueness Theorem

<p style='text-indent:20px;'>We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their <inline-formula><tex-math id="M1">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its <inline-formula><tex-math id="M2">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their <inline-formula><tex-math id="M3">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths.</p>

The one-sided dyadic Hardy—Littlewood maximal operator

2014 ◽  
Vol 144 (5) ◽  
pp. 991-1006
Author(s):  
María Lorente ◽  
Francisco J. Martín-Reyes
Keyword(s):  
Maximal Operator ◽  
Weighted Inequalities ◽  
The One ◽  
Littlewood Maximal Operator

The main aim of this paper is to introduce an appropriate dyadic one-sided maximal operator , smaller than the one-sided Hardy–Littlewood maximal operator M+ but such that it controls M+ in a similar way to how the usual dyadic maximal operator controls the Hardy-Littlewood maximal operator. We characterize the weighted inequalities for this dyadic one-sided maximal operator.

scholarly journals Regularity of Commutators of the One-Sided Hardy-Littlewood Maximal Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Daiqing Zhang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Functions ◽  
Regularity Properties ◽  
Discrete Analogues ◽  
The One ◽  
Derivatives Of

In this paper, the regularity properties of two classes of commutators of the one-sided Hardy-Littlewood maximal functions and their fractional variants are investigated. Some new bounds for the derivatives of the above commutators and the boundedness and continuity for the above commutators on the Sobolev spaces will be presented. The corresponding results for the discrete analogues are also considered.

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