scholarly journals Some inequalities for the multilinear singular integrals with Lipschitz functions on weighted Morrey spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ferit Gürbüz
Keyword(s):  
Singular Integrals ◽  
Morrey Spaces ◽  
Lipschitz Functions ◽  
Weighted Morrey Spaces ◽  
Multilinear Singular Integrals

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 Variation Inequalities for One-Sided Singular Integrals and Related Commutators

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 876
Author(s):  
Feng Liu ◽  
Seongtae Jhang ◽  
Sung-Kwun Oh ◽  
Zunwei Fu
Keyword(s):  
Singular Integrals ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Variation Operators

We establish one-sided weighted endpoint estimates for the ϱ -variation ( ϱ > 2 ) operators of one-sided singular integrals under certain priori assumption by applying one-sided Calderón–Zygmund argument. Using one-sided sharp maximal estimates, we further prove that the ϱ -variation operators of related commutators are bounded on one-sided weighted Lebesgue and Morrey spaces. In addition, we also show that these operators are bounded from one-sided weighted Morrey spaces to one-sided weighted Campanato spaces. As applications, we obtain some results for the λ -jump operators and the numbers of up-crossings. Our main results represent one-sided extensions of many previously known ones.

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