Displaying similar documents to “An oscillatory singular integral operator with polynomial phase”

L boundedness of a singular integral operator.

Dashan Fan, Yibiao Pan (1997)

Publicacions Matemàtiques

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In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t). We also obtain certain Hardy type inequalities related to this operator.

Oscillatory singular integrals on weighted Hardy spaces

Yue Hu (1992)

Studia Mathematica

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Let T f ( x ) = p . v . ʃ ¹ e i P ( x - y ) f ( y ) / ( x - y ) d y , where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.

On singular integrals of Calderón-type in R and BMO.

Steve Hofmann (1994)

Revista Matemática Iberoamericana

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We prove Lp (and weighted Lp) bounds for singular integrals of the form p.v.  ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy, where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the...

L 2 and L p estimates for oscillatory integrals and their extended domains

Yibiao Pan, Gary Sampson, Paweł Szeptycki (1997)

Studia Mathematica

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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.

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...