On weighted weak type norm inequalities for one-sided oscillatory singular integrals

Zunwei Fu; Shanzhen Lu; Shuichi Sato; Shaoguang Shi

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Displaying similar documents to “On weighted weak type norm inequalities for one-sided oscillatory singular integrals”

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

Boundedness criterion for multilinear oscillatory integrals with rough kernels

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We study a multilinear oscillatory integral with rough kernel and establish a boundedness criterion.

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Estimates for oscillatory singular integrals on Hardy spaces

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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...

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We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.

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An improved multiple Cotlar inequality is obtained. From this result, weighted norm inequalities for the maximal operator of a multilinear singular integral including weak and strong estimates are deduced under the multiple weights constructed recently.

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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.

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