Interpolation of Besov spaces of variable order of differentiation (Q1262502)

The main result: Let \(s_ 1,s_ 2\in (-\infty,\infty)\), \(s_ 0\neq s_ 1\); \(q,q_ 0,q_ 1\in [1,\infty]\), \(\theta\in (0,1)\), \(s=(1-\theta)s_ 0+\theta s_ 1\), then \[ (B^{s_ 0,a}_{p,q_ 0};B^{s_ 1,a}_{p,q_ 1})_{\theta,q}=B^{s,a}_{p,q}. \] Here \(B^{s,a}_{p,q}\) is the Besov space generated by the decomposition of \(R^ n_ x\times R^ n_{\xi}\) which is induced by the symbol a(x,\(\xi)\) of an appropriate PDO, instead of the usual resolution of unity \(\{\phi_ j(\xi)\}^{\infty}_{j=0}\) connected with the symbol \(| \xi |^ 2\) of the operator \(-\Delta.\)