Let (X, d, μ) be a space of homogeneous type equipped with a distance d and a measure μ. Assume that L is a closed linear operator which generates an analytic semigroup e-tL, t > 0. Also assume that L has a bounded H∞-calculus on L2(X) and satisfies the Lp -Lq semigroup estimates (which is weaker than the pointwise Gaussian or Poisson heat kernel bounds). The aim of this paper is to establish a theory of inhomogeneous Besov spaces associated to such an operator L. We prove the molecular decompositions for the new Besov spaces and obtain the boundedness of the fractional powers (I + L)-γ, γ > 0 on these Besov spaces. Finally, we carry out a comparison between our new Besov spaces and the classical Besov spaces.
|Number of pages||44|
|Journal||Advances in Differential Equations|
|Publication status||Published - 2017|