## Abstract

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

*L*

^{2}(

*X*) and satisfies the

*L*-

^{p}*L*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

^{q}*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.

Original language | English |
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Pages (from-to) | 191-234 |

Number of pages | 44 |

Journal | Advances in Differential Equations |

Volume | 22 |

Issue number | 3-4 |

Publication status | Published - 2017 |