Rough singular integrals associated to polynomial curves

Abstract

AbstractIn this paper, the authors establish the boundedness of singular integral operators associated to polynomial curves as well as the related maximal operators with rough kernels $\Omega \in H^{1}({\mathrm{S}}^{n-1})$ Ω ∈ H 1 ( S n − 1 ) and $h\in \Delta _{\gamma }(\mathbb{R}_{+})$ h ∈ Δ γ ( R + ) for some $\gamma >1$ γ > 1 on the Triebel–Lizorkin spaces. It should be pointed out that the bounds are independent of the coefficients of the polynomials in the definition of the operators. The main results of this paper not only improve and generalize essentially some known results but also complement some recent boundedness results.