与广义Schr?dinger算子相关的Marcinkiewicz积分（英文）

Marcinkiewicz Integrals Associated with Generalized Schr?dinger Operators

令L=-△+μ为R^n上的广义Schr?dinger算子,n≥3,其中μ≠0是满足尺度不变Kato条件和双倍条件的非负Radon测度.本文使用经典不等式估计,利用变指标和附加函数的性质,证明了与广义Schrodinger算子相关的Marcinkiewicz积分算子在变指标Herz-Morrey空间上是有界的.

Let L =-△ +μ be the generalized Schrodinger operator on R^n, n≥ 3, whereμ≠0 is a nonnegative Radon measure satisfying certain scale-invariant Kato condition and doubling condition. In this paper, using the classical inequalities, by the properties of the variable exponents and the auxiliary functions, we show that the Marcinkiewicz integral operator associated with generalized Schrodinger operator is bounded on Herz-Morrey spaces with variable exponents.