Hardy spaces and oscillatory singular integrals.
Yibiao Pan (1991)
Revista Matemática Iberoamericana
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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.
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...
E. M. Stein (1984-1985)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Hussain Mohammad Al-Qassem, Leslie Cheng, Yibiao Pan (2014)
Studia Mathematica
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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.
Josfina Alvarez, Jorge Hounie (1999)
Studia Mathematica
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We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.
Yue Hu (1992)
Studia Mathematica
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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.
Yibiao Pan, Christopher D. Sogge (1990)
Colloquium Mathematicae
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G. Sampson (1998)
Colloquium Mathematicae
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David McMichael (1993)
Mathematica Scandinavica
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Dashan Fan, Yibiao Pan (1996)
Manuscripta mathematica
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Zunwei Fu, Shanzhen Lu, Shuichi Sato, Shaoguang Shi (2011)
Studia Mathematica
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We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities for a class of one-sided oscillatory singular integrals with smooth kernel.
Harri Ojanen (2000)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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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.