Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

Mohammed Ali, Qutaibeh Katatbeh
2020 Demonstratio Mathematica  
AbstractIn this article, we study the generalized parabolic parametric Marcinkiewicz integral operators { {\mathcal M} }_{{\Omega },h,{\Phi },\lambda }^{(r)} related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω
more » ... ker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.
doi:10.1515/dema-2020-0004 fatcat:uhkvmbp6x5ftjirindjwqab2l4