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1
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On the weak (1,1) boundedness of a class of oscillatory singular integrals

100%
Pan Y.
Studia Mathematica
|
1993
|
tom 106
|
nr 3
279-287
EN
We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include $ϕ(x) = e^{-1/x^2}$ and $ϕ(x) = xe^{-1/|x|}$. Some related counterexample is also discussed.
2
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A note on a conjecture of D. Oberlin

100%
Pan Y.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 1
23-27
3
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Boundedness of certain oscillatory singular integrals

64%
Fan D., Pan Y.
Studia Mathematica
|
1995
|
tom 114
|
nr 2
105-116
EN
We prove the $L^p$ and $H^1$ boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where $Ω(x) = e^{iΦ(x)}K(x)$, K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.
4
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Rough oscillatory singular integrals on ℝⁿ

51%
Al-Qassem H., Cheng L., Pan Y.
Studia Mathematica
|
2014
|
tom 221
|
nr 3
249-267
EN
We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.
5
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Estimates for oscillatory singular integrals on Hardy spaces

51%
Al-Qassem H., Cheng L., Pan Y.
Studia Mathematica
|
2014
|
tom 224
|
nr 3
277-289
EN
For any n ∈ ℕ, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space H¹(ℝⁿ). Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the H¹ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown to be valid on weighted Hardy spaces as well if the weights belong to the Muckenhoupt class A₁.
6
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$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

51%
Pan Y., Sampson G., Szeptycki P.
Studia Mathematica
|
1997
|
tom 122
|
nr 3
201-224
EN
We prove the $L^p$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function $|x|^{α}|y|^{β}$. Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
7
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Oscillatory integrals associated to folding canonical relations

51%
Pan Y., Sogge C. D.
Colloquium Mathematicum
|
1990
|
tom 60-61
|
nr 2
413-419
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