Heat Kernels and Besov Spaces Associated with Second Order Divergence Form Elliptic Operators

Cao J, Grigoryan A. Heat Kernels and Besov Spaces Associated with Second Order Divergence Form Elliptic Operators. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2020;26(1): 3.Let L=-div(A backward difference be a uniformly elliptic operator in Rn with real, symmetric, measurable coefficients. We study the identity of two families of Besov spaces Bp,qs,L and Bp,qs , where the former one is defined using the heat semigroup of L , while the latter one is defined in a classical way, using the metric structure of Rn. A sharp range of parameters p, q, s ensuring the identity Bp,qs,L=Bp,qs {L}}}=B_{p,q}{s}$$\end{document} is given by a Hardy-Littlewood-Sobolev-Kato diagram