Quantitative Weighted Bounds for Littlewood-Paley Functions Generated by Fractional Heat Semigroups Related with Schrodinger Operators

Let L = -? + V be a Schrodinger operator on ]Rn, where ? denotes the Laplace operator ?(n)(i=1)?(2)/?x(i )(2)and V is a nonnegative potential belonging to a certain reverse Holder class RHq(R-n)with q > n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood-Paley functions generated by fractional heat semigroups related with the Schrodinger operators.

Automated summary

In this paper, we establish the quantitative weighted boundedness of Littlewood-Paley functions generated by fractional heat semigroups related with the Schrodinger operators, using the regularity estimate of the fractional heat kernel related with L.