Rough Marcinkiewics integral operators.
Rough singular integrals on product spaces.
On the boundedness of rough parametric Marcinkiewicz functions.
On certain rough integral operators and extrapolation.
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.
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...
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.
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