Properties of the Sobolev space $H_k^{s,s'}$

Volume 71 / 1999

Henryk Kołakowski Annales Polonici Mathematici 71 (1999), 199-209 DOI: 10.4064/ap-71-2-199-209


Let n ≥ 2 and $H_k^{s,s'} = {u∈ S'(ℝ^n): ∥u∥_{s,s'} < ∞}$, where $∥u∥²_{s,s'} = (2π)^{-n} ∫(1+|ξ|²)^s (1+|ξ'|²)^{s'}|Fu(ξ)|²dξ $, $Fu(ξ) = ∫e^{-ixξ} u(x) dx$, $ξ'∈ ℝ^k$, k < n. We prove that for some s,s' the space $H^{s,s'}_k$ is a multiplicative algebra.


  • Henryk Kołakowski

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