Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

2018 ◽  
Vol 291 (8-9) ◽  
pp. 1400-1417 ◽  
Author(s):  
Idha Sihwaningrum ◽  
Hendra Gunawan ◽  
Eiichi Nakai
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Fractional Integral Operators ◽  
Generalized Morrey Spaces ◽  
Measure 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].

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.

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