Sharp Trudinger Type Inequalities for Measure-Valued Lagrangeans
The aim of the paper is to prove weighted John-Nirenberg and sharp Trudinger type inequalities for measure-valued (α, p)-Lagrangeans.
Doubling measure
Sharp Lp estimates for Schrödinger groups on spaces of homogeneous type
We prove an Lp estimate (Equation Presented) for the Schrödinger group generated by a semibounded, self-adjoint operator L on a metric measure space X of homogeneous type (where n is the doubling dimension of X). The assumptions on L are a mild Lp0 → Lp' 0 smoothing estimate and a mild L2 → L2 off-diagonal estimate for the corresponding heat kernel e -tL. The estimate is uniform for φ varying in bounded sets of S(R), or more generally of a suitable weighted Sobolev space.