Advances in Differential Equations

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

The Anh Bui and Xuan Duong

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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

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

First available in Project Euclid: 18 February 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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