The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups

Abstract EN

Assume that G is a stratified Lie group and Q is the homogeneous dimension of G.

Let -Δ be the sub-Laplacian on G and W≢0 a nonnegative potential belonging to certain reverse Hölder class Bs for s≥Q/2.

Let L=-Δ+W be a Schrödinger operator on the stratified Lie group G.

In this paper, we prove the boundedness of some integral operators related to L, such as L-1∇2, L-1W, and L-1(-Δ) on the space BMOL(G).