Hardy spaces and oscillatory singular integrals.
Yibiao Pan (1991)
Revista Matemática Iberoamericana
Similarity:
Yibiao Pan (1991)
Revista Matemática Iberoamericana
Similarity:
Dashan Fan, Yibiao Pan (1997)
Publicacions Matemàtiques
Similarity:
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.
Yue Hu (1992)
Studia Mathematica
Similarity:
Let , where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.
Shuichi Sato (2000)
Studia Mathematica
Similarity:
We consider the -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
Margaret Murray (1987)
Studia Mathematica
Similarity:
Leslie C. Cheng, Yibiao Pan (2000)
Publicacions Matemàtiques
Similarity:
We prove the uniform H boundedness of oscillatory singular integrals with degenerate phase functions.
Steve Hofmann (1994)
Revista Matemática Iberoamericana
Similarity:
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...
Robert Fefferman (1985)
Revista Matemática Iberoamericana
Similarity:
Josefina Alvarez (1998)
Collectanea Mathematica
Similarity:
Yibiao Pan, Gary Sampson, Paweł Szeptycki (1997)
Studia Mathematica
Similarity:
We prove the 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 . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
Hussain Al-Qassem, Leslie Cheng, Yibiao Pan (2014)
Studia Mathematica
Similarity:
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...