scholarly journals A characterization for fractional integral and its commutators in Orlicz and generalized Orlicz–Morrey spaces on spaces of homogeneous type

2019 ◽  
Vol 9 (4) ◽  
pp. 1991-2019 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Fatih Deringoz
Keyword(s):  
Fractional Integral ◽  
Morrey Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

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 Pointwise Multipliers on Weak Morrey Spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 363-381
Author(s):  
Ryota Kawasumi ◽  
Eiichi Nakai
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Pointwise Multipliers ◽  
Weak Lebesgue Space ◽  
Weak Morrey Spaces

Abstract We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.

Two-weighted inequalities for maximal operators related to Schrödinger differential operator

2020 ◽  
Vol 32 (6) ◽  
pp. 1415-1439
Author(s):  
Maria Amelia Vignatti ◽  
Oscar Salinas ◽  
Silvia Hartzstein
Keyword(s):  
Fractional Integral ◽  
Schrödinger Operators ◽  
Finite Measure ◽  
The Other ◽  
Maximal Operators ◽  
Schrodinger Operators ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Spaces Of Homogeneous Type ◽  
Measure Spaces

AbstractWe introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.

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