Phase Space Analysis for the Heat Equation

Abstract

This chapter explains in an elementary way via the Cauchy problem for the heat equation without with and mass term how phase space analysis and interpolation techniques can be used to prove L ^p − L ^q estimates on and away from the conjugate line $\frac {1}{p}+\frac {1}{q}=1$, p ∈ [1, ∞]. Here we distinguish between L ^p − L ^q estimates for low regular and for large regular data.