Carleson Measure Associated with the Fractional Heat Semigroup of Schrödinger Operator (Communications in Mathematical Research, 2024)
Let $L=−∆+V$ be a Schrödinger operator, where $∆$ is the Laplacianon $\mathbb{R}^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $B_{d/2}.$ In this paper, we define a new version of Carleson measure associated with thefractional heat semigroup of Schrödinger operator $L.$ We will characterize theCampanato spaces and the predual spaces of the Hardy spaces by the newCarleson measure.
Keywords: Schrödinger operator; reverse Hölder class; Carleson measure; fractional heat semigroup; Campanato spaces.