Boundedness of operators generated by fractional semigroups associated with Schrödinger operators on Campanato type spaces via $T1$ theorem

Abstract

Let L = −∆ + V be a Schrödinger operator, where the nonnegative potential V belongs to the reverse Hölder class B q . By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, {e −tL α } t>0 , associated with L. As an application, we obtain the BMO γ L -boundedness of the maximal function, and the Littlewood-Paley g-functions associated with L via T 1 theorem, respectively.In the research of harmonic analysis and partial differential equations, the maximal operators and Littelwood-Paley g-functions paly an important role and were investigated by many mathematicians extensively. For any integrable function f on R n , the P.