scholarly journals OSCILLATORY INTEGRAL OPERATORS AND THEIR COMMUTATORS IN MODIFIED WEIGHTED MORREY SPACES WITH VARIABLE EXPONENT

2019 ◽  
Vol 32 (3) ◽  
Author(s):  
J.J. Hasanov ◽  
A.M. Musayev
Keyword(s):  
Variable Exponent ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Oscillatory Integral Operators

scholarly journals Boundedness of Oscillatory Integrals with Variable Calderón-Zygmund Kernel on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yali Pan ◽  
Changwen Li ◽  
Xinsong Wang
Keyword(s):  
Harmonic Analysis ◽  
Singular Integrals ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Morrey Spaces ◽  
Oscillatory Integrals ◽  
Weighted Morrey Spaces ◽  
Oscillatory Integral Operators ◽  
Oscillatory Singular Integrals

Oscillatory integral operators play a key role in harmonic analysis. In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on the weighted Morrey spacesLp,k(ω). Meanwhile, the corresponding results for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.

scholarly journals Boundedness of Fractional Oscillatory Integral Operators and Their Commutators in Vanishing Generalized Weighted Morrey Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Bilal Çekiç ◽  
Ayşegül Çelik Alabalık
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Morrey Spaces ◽  
Integral Inequalities ◽  
Weighted Morrey Spaces ◽  
Oscillatory Integral Operators ◽  
Type Integral

In this article, we give the boundedness conditions in terms of Zygmund-type integral inequalities for oscillatory integral operators and fractional oscillatory integral operators on the vanishing generalized weighted Morrey spaces. Moreover, we investigate corresponding commutators.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

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