In this paper, we study the the parabolic Marcinkiewicz integral [...] MΩ,hρ1,ρ2 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.
Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded P-compactly packed modules and we give a number of results concerning such graded modules. In fact, our objective is to investigate graded P-compactly packed modules and examine in particular when graded R-modules are P-compactly packed. Finally, we introduce the concept of graded finitely P-compactly packed modules and give a number of its properties.
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