On the Traces of Means of Spectral Expansions Corresponding to Elliptic Pseudodifferential Operators for Continuous Functions in Liouville and Nikol'skii–Besov Classes

摘要

Let Cl be an arbitrary iV-dimensional domain with C~∞ boundary or Ω = R~N. We define the symbol class S~m(Ω) as the set of functions a(x,y) ∈ C~∞ (Ω * {R~N0}) such that the inequality [D_x~αD_y~βa(x,y)| ≤ const * (1 + |y|)~(m-|β|) with a constant independent of x ∈ K and y ∈ R0 is valid for each compact set K is contained in in contained in Cl and for arbitrary multi-indices α and β.