Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces

2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Seymur S. Aliev ◽  
Vagif S. Guliev
Keyword(s):  
Integral Operator ◽  
Morrey Spaces ◽  
Marcinkiewicz Integral ◽  
Generalized Morrey Spaces ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Integral Operator

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.

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.

scholarly journals Morrey Spaces for Nonhomogeneous Metric Measure Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cao Yonghui ◽  
Zhou Jiang
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Definition Of

The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.

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 On the boundedness of a generalized fractional integral on generalized Morrey spaces

2002 ◽  
Vol 33 (4) ◽  
pp. 335-340
Author(s):  
Eridani Eridani
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Campanato Space ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Generalized Fractional Integral

In this paper we extend Nakai's result on the boundedness of a generalized fractional integral operator from a generalized Morrey space to another generalized Morrey or Campanato space.

scholarly journals Riesz potential, Marcinkiewicz integral and their commutators on mixed Morrey spaces

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 931-944
Author(s):  
Andrea Scapellato
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Riesz Potential ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Higher Order ◽  
Lipschitz Class ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Type Integral

This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,I?], where I? denotes the fractional integral operator of order ? and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b,I?]k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral ?? and the commutator [b,??] when b belongs to the BMO class.

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