Dunkl Translation and Uncentered Maximal Operator on the Real Line

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2007/87808 ◽

2007 ◽

Vol 2007 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Chokri Abdelkefi ◽

Mohamed Sifi

Keyword(s):

Characteristic Function ◽

Real Line ◽

Maximal Operator ◽

Weak Type ◽

Dunkl Operator ◽

The Real

We establish estimates of the Dunkl translation of the characteristic functionχ[−ɛ,ɛ],ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type(1,1). As a consequence, we obtain theLp-boundedness of this operator for1<p≤+∞.

(Lp,Lq) Boundedness of the fractional maximal operator associated with the Dunkl operator on the real line

Integral Transforms and Special Functions ◽

10.1080/10652460903507248 ◽

2010 ◽

Vol 21 (8) ◽

pp. 629-639 ◽

Cited By ~ 2

Author(s):

V. S. Guliyev ◽

Y. Y. Mammadov

Keyword(s):

Real Line ◽

Maximal Operator ◽

Dunkl Operator ◽

The Real ◽

Fractional Maximal Operator

Weighted inequalities for a maximal function on the real line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500000871 ◽

2001 ◽

Vol 131 (2) ◽

pp. 267-277 ◽

Cited By ~ 3

Author(s):

A. L. Bernardis ◽

F. J. Martín-Reyes

Keyword(s):

Maximal Function ◽

Real Line ◽

Maximal Operator ◽

Singular Integrals ◽

Weak Type ◽

Weighted Inequalities ◽

Strong Type ◽

The Real ◽

Image Position ◽

Cesaro Convergence

We consider the maximal operator defined on the real line by which is related to the Cesàro convergence of the singular integrals. We characterize the weights w for which Mα is of weak type, strong type and restricted weak type (p, p) with respect to the measure w(x) dx.

Besov-type spaces for the Dunkl operator on the real line

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2005.06.054 ◽

2007 ◽

Vol 199 (1) ◽

pp. 56-67 ◽

Cited By ~ 7

Author(s):

Lotfi Kamoun

Keyword(s):

Real Line ◽

Dunkl Operator ◽

The Real ◽

Type Spaces ◽

Besov Type Spaces

Best constants in some estimates for the harmonic maximal operator on the real line

Colloquium Mathematicum ◽

10.4064/cm8213-4-2020 ◽

2021 ◽

Vol 164 (1) ◽

pp. 133-148

Author(s):

Łukasz Kamiński ◽

Adam Osękowski

Keyword(s):

Real Line ◽

Maximal Operator ◽

Best Constants ◽

The Real

On fractional maximal function and fractional integrals associated with the Dunkl operator on the real line

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.11.083 ◽

2009 ◽

Vol 353 (1) ◽

pp. 449-459 ◽

Cited By ~ 6

Author(s):

Vagif S. Guliyev ◽

Yagub Y. Mammadov

Keyword(s):

Maximal Function ◽

Real Line ◽

Fractional Integrals ◽

Dunkl Operator ◽

The Real ◽

Fractional Maximal Function

Sonine-type integral transforms related to the Dunkl operator on the real line

Integral Transforms and Special Functions ◽

10.1080/10652460903024251 ◽

2009 ◽

Vol 20 (12) ◽

pp. 915-924 ◽

Cited By ~ 1

Author(s):

Mohamed Ali Mourou

Keyword(s):

Real Line ◽

Integral Transforms ◽

Dunkl Operator ◽

The Real ◽

Type Integral

Fractional maximal commutator on Orlicz spaces for the Dunkl operator on the real line

Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan ◽

10.29228/proc.51 ◽

2020 ◽

Vol 4 (4) ◽

pp. 130-144

Author(s):

Yagub Y. Mammadov - Fatma A. Muslumova - Zaman V. Safarov

Keyword(s):

Real Line ◽

Orlicz Spaces ◽

Dunkl Operator ◽

The Real

Remarks on the Hardy–Littlewood maximal function

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500027116 ◽

1998 ◽

Vol 128 (1) ◽

pp. 1-9 ◽

Cited By ~ 6

Author(s):

J. M. Aldaz

Keyword(s):

Maximal Function ◽

Real Line ◽

Weak Type ◽

Best Constant ◽

The Real ◽

Littlewood Maximal Function

We answer questions of A. Carbery, M. Trinidad Menárguez and F. Soria by proving, firstly, that for the centred Hardy–Littlewood maximal function on the real line, the best constant C for the weak type (1, 1) inequality is strictly larger than 3/2, and secondly, that C is strictly less than 2 (known to be the best constant in the noncentred case).

Centered Hardy–Littlewood maximal operator on the real line: Lower bounds

Comptes Rendus Mathematique ◽

10.1016/j.crma.2019.03.003 ◽

2019 ◽

Vol 357 (4) ◽

pp. 339-344 ◽

Cited By ~ 2

Author(s):

Paata Ivanisvili ◽

Samuel Zbarsky

Keyword(s):

Lower Bounds ◽

Real Line ◽

Maximal Operator ◽

The Real ◽

Littlewood Maximal Operator

Maximal functions for Weinstein operator

Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica ◽

10.2478/aupcsm-2020-0009 ◽

2020 ◽

Vol 19 (1) ◽

pp. 105-119

Author(s):

Chokri Abdelkefi

Keyword(s):

Characteristic Function ◽

Harmonic Analysis ◽

Large Class ◽

Half Space ◽

Maximal Function ◽

Maximal Operator ◽

Weak Type ◽

Closed Ball ◽

Heat Semigroup ◽

Poisson Semigroup

AbstractIn the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ɛ centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.