Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers

Xuan Thinh Duong, Adam Sikora, Lixin Yan

Let $L$ be a non-negative self adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type. Assume that $L$ generates a holomorphic semigroup $e^{-tL}$ whose kerne…