Title: Local Hardy spaces with variable exponents associated to non-negative self-adjoint operators satisfying Gaussian estimates,
Abstract: In this paper we introduce variable exponent local Hardy spaces associated
with a non-negative self-adjoint operator L. We define them by using an area
square integral involving the heat semigroup associated to L. A molecular
characterization is established and as an aplication of the molecular
characterization we prove that our local Hardy space coincides with the
(global) variable exponent Hardy space associated to L, provided that 0 does
not belong to the spectrum of L. Also, we show that it coincides with the
global variable exponent Hardy space associated to L+I.