Parabolic Marcinkiewicz integrals on product spaces and extrapolation

Abstract

In this paper, we study the the parabolic Marcinkiewicz integral MΩ,hρ1,ρ2${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

Keywords

• lp boundedness
• parabolic marcinklewicz integrals
• rough kernels
• product spaces
• 40b20
• 40b15
• 40b25