Uniform boundedness of oscillatory singular integrals on Hardy spaces.
Leslie C. Cheng, Yibiao Pan (2000)
Publicacions Matemàtiques
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We prove the uniform H boundedness of oscillatory singular integrals with degenerate phase functions.
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Leslie C. Cheng, Yibiao Pan (2000)
Publicacions Matemàtiques
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We prove the uniform H boundedness of oscillatory singular integrals with degenerate phase functions.
Yibiao Pan (1991)
Revista Matemática Iberoamericana
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Wengu Chen, Shanzhen Lu (2004)
Studia Mathematica
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We study a multilinear oscillatory integral with rough kernel and establish a boundedness criterion.
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.
Miroslav Bartušek (2001)
Mathematica Slovaca
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David McMichael (1993)
Mathematica Scandinavica
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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...
G. Sampson (1998)
Colloquium Mathematicae
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Yibiao Pan, Christopher D. Sogge (1990)
Colloquium Mathematicae
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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 , which are essential improvements of some well known results, are given.
Dashan Fan, Yibiao Pan (1996)
Manuscripta mathematica
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E. M. Stein (1984-1985)
Séminaire Équations aux dérivées partielles (Polytechnique)
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E.M. Stein, D.H. Phong (1992)
Inventiones mathematicae
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