Generalized Parabolic Marcinkiewicz Integral Operators Related to Surfaces of Revolution

Abstract

In this work, the generalized parametric Marcinkiewicz integral operators with mixed homogeneity related to surfaces of revolution are studied. Under some weak conditions on the kernels, the boundedness of such operators from Triebel–Lizorkin spaces to L p spaces are established. Our results, with the help of an extrapolation argument, improve and extend some previous known results.

A Note on Parabolic Maximal Operators along Surfaces of Revolution via Extrapolation

“…We point out that under some specific constraints, the operator µ (γ) P,Θ,ϕ was investigated in [11,12,[26][27][28][29][30].…”