scholarly journals Boundedness of One-Sided Oscillatory Integral Operators on Weighted Lebesgue Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zunwei Fu ◽  
Shanzhen Lu ◽  
Yibiao Pan ◽  
Shaoguang Shi
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Lebesgue Spaces ◽  
Oscillatory Integral Operators ◽  
Weighted Lebesgue Spaces ◽  
Interpolation Of Operators ◽  
Change Of Measures

We consider one-sided weight classes of Muckenhoupt type, but larger than the classical Muckenhoupt classes, and study the boundedness of one-sided oscillatory integral operators on weighted Lebesgue spaces using interpolation of operators with change of measures.

FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES

2018 ◽  
Vol 61 (1) ◽  
pp. 231-248 ◽  
Author(s):  
KWOK-PUN HO
Keyword(s):  
Banach Function Space ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Banach Function Spaces ◽  
Oscillatory Integral Operators ◽  
Interpolation Functor ◽  
The Laplace Transform ◽  
Fourier Type

AbstractWe establish the mapping properties of Fourier-type transforms on rearrangement-invariant quasi-Banach function spaces. In particular, we have the mapping properties of the Laplace transform, the Hankel transforms, the Kontorovich-Lebedev transform and some oscillatory integral operators. We achieve these mapping properties by using an interpolation functor that can explicitly generate a given rearrangement-invariant quasi-Banach function space via Lebesgue spaces.

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.

scholarly journals Damping estimates for oscillatory integral operators with real-analytic phases and its applications

2019 ◽  
Vol 31 (4) ◽  
pp. 843-865
Author(s):  
Zuoshunhua Shi ◽  
Shaozhen Xu ◽  
Dunyan Yan
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Independent Interest ◽  
One Dimensional ◽  
Oscillatory Integral Operators ◽  
Real Analytic

Abstract In this paper, we investigate sharp damping estimates for a class of one-dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give a new proof of the sharp {L^{p}} estimates, which have been proved by Xiao in [Endpoint estimates for one-dimensional oscillatory integral operators, Adv. Math. 316 2017, 255–291]. The damping estimates obtained in this paper are of independent interest.

scholarly journals On Wiener’s Tauberian theorems and convolution for oscillatory integral operators

2019 ◽  
Vol 43 (3) ◽  
pp. 1124-1147 ◽  
Author(s):  
Luis Pinheiro de CASTRO ◽  
Rita Correia GUERRA ◽  
Nguyen Minh TUAN
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Tauberian Theorems ◽  
Oscillatory Integral Operators

Bounds on oscillatory integral operators

2011 ◽  
Vol 349 (3-4) ◽  
pp. 137-141 ◽  
Author(s):  
Jean Bourgain ◽  
Lawrence Guth
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Oscillatory Integral Operators
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