scholarly journals Commutator of fractional integral with Lipschitz functions associated with Schrödinger operator on local generalized Morrey spaces

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Vagif S. Guliyev ◽  
Ali Akbulut
Keyword(s):  
Schrödinger Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Lipschitz Functions ◽  
Schrodinger Operator ◽  
Generalized Morrey Spaces

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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