scholarly journals The Riesz “rising sun” lemma for arbitrary Borel measures with some applications

2007 ◽  
Vol 5 (3) ◽  
pp. 319-331
Author(s):  
Lasha Ephremidze ◽  
Nobuhiko Fujii ◽  
Yutaka Terasawa
Keyword(s):  
Real Line ◽  
Maximal Operator ◽  
Type Inequality ◽  
Exact Constant ◽  
Locally Finite ◽  
The Real ◽  
Borel Measures ◽  
Littlewood Maximal Operator

The Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak(1,1)type inequality for the corresponding Hardy-Littlewood maximal operator.

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

2021 ◽  
Vol 164 (1) ◽  
pp. 133-148
Author(s):  
Łukasz Kamiński ◽  
Adam Osękowski
Keyword(s):  
Real Line ◽  
Maximal Operator ◽  
Best Constants ◽  
The Real

Weighted Lorentz norm inequalities for general maximal operators associated with certain families of Borel measures

1998 ◽  
Vol 128 (2) ◽  
pp. 403-424 ◽  
Author(s):  
María Dolores Sarrión Gavilán
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Weighted Inequalities ◽  
General Measure ◽  
Norm Inequalities ◽  
Fractional Maximal Operator ◽  
Borel Measures ◽  
The One ◽  
Littlewood Maximal Operator ◽  
Lorentz Norm

Given a certain family ℱ of positive Borel measures and γ ∈ [0, 1), we define a general onesided maximal operatorand we study weighted inequalities inLp,qspaces for these operators. Our results contain, as particular cases, the characterisation of weighted Lorentz norm inequalities for some well-known one-sided maximal operators such as the one-sided Hardy–Littlewood maximal operator associated with a general measure, the one-sided fractional maximal operatorand the maximal operatorassociated with the Cesèro-α averages.

scholarly journals Dunkl Translation and Uncentered Maximal Operator on the Real Line

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
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≤+∞.

σ-FINITE BOREL MEASURES ON THE REAL LINE

1997 ◽  
Vol 23 (1) ◽  
pp. 185 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real ◽  
Borel Measures

Weighted inequalities for a maximal function on the real line

2001 ◽  
Vol 131 (2) ◽  
pp. 267-277 ◽  
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.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real
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