Rough singular integrals and maximal operators with mixed homogeneity along compound curves

Abstract

The parabolic singular integrals along certain compound curves as well as the related maximal operators are considered. Under rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp‐mapping properties for such operators are established. Some previous results are greatly extended and improved.

Boundedness and Continuity of Several Integral Operators with Rough Kernels inWFβSn-1Liu1 2018Journal of Function SpacesSelf Cite1020View full textAdd to dashboardCite

“…More precisely, the above authors established the bounds for ℎ,Ω with |1/ − 1/2| < 1/ max{2, } − 1/ if ℎ ∈ Δ (R + ) for > 1 and Ω ∈ F (S −1 ) for some > max{ , 2}. Recently, Liu and Wu [7] extended the result of [1] to the singular integrals along polynomial compound curves in the mixed homogeneity setting.…”