Advances in Differential Equations

Inhomogeneous Besov spaces associated to operators with off-diagonal semigroup estimates

The Anh Bui and Xuan Duong

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let $(X, d, \mu)$ be a space of homogeneous type equipped with a distance $d$ and a measure $\mu$. Assume that $L$ is a closed linear operator which generates an analytic semigroup $e^{-tL}, t > 0$. Also assume that $L$ has a bounded $H_\infty$-calculus on $L^2(X)$ and satisfies the $L^p-L^q$ 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 $(I+L)^{-\gamma}, \gamma > 0$ on these Besov spaces. Finally, we carry out a comparison between our new Besov spaces and the classical Besov spaces.

Article information

Source
Adv. Differential Equations Volume 22, Number 3/4 (2017), 191-234.

Dates
First available in Project Euclid: 18 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1487386867

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Citation

Bui, The Anh; Duong, Xuan. Inhomogeneous Besov spaces associated to operators with off-diagonal semigroup estimates. Adv. Differential Equations 22 (2017), no. 3/4, 191--234.https://projecteuclid.org/euclid.ade/1487386867


Export citation