Lp-Improving Properties for Some Measures Supported on Curves.
On the weak (1,1) boundedness of a class of oscillatory singular integrals
We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include and . Some related counterexample is also discussed.
A note on a conjecture of D. Oberlin
Hardy spaces and oscillatory singular integrals.
The Complete (L..., L...) Mapping Properties for a Class of Oscillatory Integrals.
Oscillatory Integrals and Atoms on the Unit sphere.
Boundedness of certain oscillatory singular integrals
We prove the and boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where , K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.
L boundedness of a singular integral operator.
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 integrals associated to folding canonical relations
and estimates for oscillatory integrals and their extended domains
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.
L estimates for singular integrals with kernels beloging to certain block spaces.
We establish the L boundedness of singular integrals with kernels which belong to block spaces and are supported by subvarities.
On certain estimates for Marcinkiewicz integrals and extrapolation.
Uniform boundedness of oscillatory singular integrals on Hardy spaces.
We prove the uniform H boundedness of oscillatory singular integrals with degenerate phase functions.
Rough oscillatory singular integrals on ℝⁿ
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.
Estimates for oscillatory singular integrals on Hardy spaces
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 to be valid...
On certain rough integral operators and extrapolation.
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