Communications in Mathematical Analysis

Besov Spaces Associated with Operators

A. Wong

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Recent work of Bui, Duong and Yan in [2] defined Besov spaces associated with a certain operator $L$ under the weak assumption that $L$ generates an analytic semigroup $e^{-tL}$ with Poisson kernel bounds on $L^2({\mathcal X})$ where ${\mathcal X}$ is a (possibly non-doubling) quasi-metric space of polynomial upper bound on volume growth. This note aims to extend certain results in [2] to a more general setting when the underlying space can have different dimensions at $0$ and infinity. For example, we make some extensions to the Besov norm equivalence result in Proposition 4.4 of [2], such as to more general class of functions with suitable decay at $0$ and infinity, and to non-integer $k\geq 1$.

Article information

Commun. Math. Anal., Volume 16, Number 2 (2014), 89-104.

First available in Project Euclid: 20 October 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B30: $H^p$-spaces 42B35: Function spaces arising in harmonic analysis 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Besov space Analytic semigroup heat kernel Embedding theorem


Wong, A. Besov Spaces Associated with Operators. Commun. Math. Anal. 16 (2014), no. 2, 89--104.

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