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.

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 A WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES OVER METRIC MEASURE SPACES

2016 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Idha Sihwaningrum
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Metric Measure Spaces ◽  
Measure Spaces

This paper presents a weak-(p, q) inequality for fractional integral operator on Morrey spaces over metric measure spaces of nonhomogeneous type. Both parameters p and q are greater than or equal to one. The weak-(p, q) inequality is proved by employing an inequality involving maximal operator on the spaces under consideration.

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.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

scholarly journals MORREY SPACES AND FRACTIONAL OPERATORS

2010 ◽  
Vol 88 (2) ◽  
pp. 247-259 ◽  
Author(s):  
HITOSHI TANAKA
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Fractional Maximal Operator

AbstractThe relation between the fractional integral operator and the fractional maximal operator is investigated in the framework of Morrey spaces. Applications to the Fefferman–Phong and the Olsen inequalities are also included.

scholarly journals A WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES VIA HEDBERG TYPE INEQUALITY

2016 ◽  
Vol 8 (2) ◽  
pp. 103
Author(s):  
Idha Sihwaningrum ◽  
Hendra Gunawan
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Morrey Spaces ◽  
Fractional Integral Operator

By employing the growth measure, in this paper we prove the weak-(p, q) inequality for fractional integral operator on Morrey spaces via Hedberg type inequality. The proof also needs the weak-(p, p) inequality of the maximal operator in the same spaces.

Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 303-311
Author(s):  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Transforms ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Fractional Integral Operators ◽  
Generalized Morrey Spaces ◽  
Measure Spaces ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Abstract In this paper, we aim to deal with the boundedness and the weak-type boundedness for the generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 2017, 2, 159–190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 2017, 7, 534–546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

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