Displaying similar documents to “Rough oscillatory singular integrals on ℝⁿ”

An estimation for a family of oscillatory integrals

Magali Folch-Gabayet, James Wright (2003)

Studia Mathematica

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Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.

Estimates for oscillatory singular integrals on Hardy spaces

Hussain Al-Qassem, Leslie Cheng, Yibiao Pan (2014)

Studia Mathematica

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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...

Boundedness of higher order commutators of oscillatory singular integrals with rough kernels

Huoxiong Wu (2005)

Studia Mathematica

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The author studies the commutators generated by a suitable function a(x) on ℝⁿ and the oscillatory singular integral with rough kernel Ω(x)|x|ⁿ and polynomial phase, where Ω is homogeneous of degree zero on ℝⁿ, and a(x) is a BMO function or a Lipschitz function. Some mapping properties of these higher order commutators on L p ( ℝ ⁿ ) , which are essential improvements of some well known results, are given.