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.

scholarly journals Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases

2019 ◽  
Vol 63 (4) ◽  
pp. 771-786
Author(s):  
Danqing He ◽  
Zuoshunhua Shi
Keyword(s):  
Critical Exponents ◽  
Homogeneous Polynomial ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Sharp Bounds ◽  
Oscillatory Integral Operators ◽  
Several Variables ◽  
Rank One ◽  
Important Notion ◽  
Additional Assumptions

AbstractWe obtain sharp $L^{p}$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition that is an important notion introduced by Greenleaf, Pramanik, and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint $L^{p}$ estimates.

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