Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary

In this note, we propose to remove some small gaps in the theory of potential spaces H _p ^s (Ω) and Besov spaces B _p ^s (Ω), 1 < p < ∞, s ∈ ℝ, for a bounded Lipschitz domain Ω ⊂ ℝ ⁿ , n ⩾ 2. Namely, we discuss 1) the unified definitions of these spaces with s of any sign, the unified duality theorems and interpolation relations, 2) the possibility of constructing a function in these spaces with given array of traces of its derivatives on the boundary. To the memory of Leonid Romanovich Volevich The work was partially supported by the RFBR grant no. 07-01-00287.