scholarly journals On the L2 boundedness of parametric Marcinkiewicz integral operator

2011 ◽  
Vol 375 (2) ◽  
pp. 745-752 ◽  
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Integral Operator ◽  
Marcinkiewicz Integral ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Integral Operator

Marcinkiewicz integral operators on product domains

2002 ◽  
Vol 132 (3) ◽  
pp. 523-530
Author(s):  
KYUNG SOO RIM
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Cancellation Property ◽  
Product Domains ◽  
Marcinkiewicz Integral Operator

With the cancellation property of the bounded kernel, we prove that the generalized Marcinkiewicz integral operator is bounded on L2 (ℝn×ℝm) for all dimensions n, m.

GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES

2016 ◽  
Vol 103 (2) ◽  
pp. 268-278 ◽  
Author(s):  
GUANGHUI LU ◽  
SHUANGPING TAO
Keyword(s):  
Integral Operator ◽  
Measure Space ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Marcinkiewicz Integral ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Measure Spaces ◽  
Definition Of ◽  
Marcinkiewicz Integral Operator

Let $({\mathcal{X}},d,\unicode[STIX]{x1D707})$ be a nonhomogeneous metric measure space satisfying the so-called upper doubling and the geometric doubling conditions. In this paper, the authors give the natural definition of the generalized Morrey spaces on $({\mathcal{X}},d,\unicode[STIX]{x1D707})$, and then investigate some properties of the maximal operator, the fractional integral operator and its commutator, and the Marcinkiewicz integral operator.

scholarly journals Higher-Order Commutators of Parametric Marcinkiewicz Integrals on Herz Spaces with Variable Exponent

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongbin Wang ◽  
Dunyan Yan
Keyword(s):  
Variable Exponent ◽  
Homogeneous Function ◽  
Higher Order ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Herz Spaces ◽  
Marcinkiewicz Integrals ◽  
Bmo Functions ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Integral Operator

LetΩ∈Ls(Sn-1)fors⩾1be a homogeneous function of degree zero andbbe BMO functions. In this paper, we obtain some boundedness of the parametric Marcinkiewicz integral operatorμΩρand its higher-order commutator[bm,μΩρ]on Herz spaces with variable exponent.

scholarly journals A boundedness result for Marcinkiewicz integral operator

2020 ◽  
Vol 18 (1) ◽  
pp. 829-836
Author(s):  
Laith Hawawsheh ◽  
Mohammad Abudayah
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Integrability Condition ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Marcinkiewicz Integral ◽  
Radial Functions ◽  
New Space ◽  
Marcinkiewicz Integral Operator ◽  
Boundedness Result

Abstract We extend a boundedness result for Marcinkiewicz integral operator. We find a new space of radial functions for which this class of singular integral operators remains {L}^{p} -bounded when its kernel satisfies only the sole integrability condition.

scholarly journals Rough Marcinkiewicz integral operators

2001 ◽  
Vol 27 (8) ◽  
pp. 495-503 ◽  
Author(s):  
Hussain Al-Qassem ◽  
Ahmad Al-Salman
Keyword(s):  
Integral Operator ◽  
Unit Sphere ◽  
Homogeneous Function ◽  
Integral Operators ◽  
Mean Value ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Polynomial Mapping ◽  
Marcinkiewicz Integral Operator ◽  
Boundedness Result

We study the Marcinkiewicz integral operatorM𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where𝒫is a polynomial mapping fromℝnintoℝdandΩis a homogeneous function of degree zero onℝnwith mean value zero over the unit sphereSn−1. We prove anLpboundedness result ofM𝒫for roughΩ.

Sign in / Sign up

Export Citation Format

Share Document