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ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

Let n ≥ 2 and

H_{k}^{s, s'} = {u \in S' (ℝ^{n}) : ∥ u ∥_{s, s'} < \infty}

, where

∥ u ∥ ²_{s, s'} = {(2 π)}^{- n} \int {(1 + | ξ | ²)}^{s} {(1 + | ξ' | ²)}^{s'} | F u (ξ) | ² d ξ

,

F u (ξ) = \int e^{- i x ξ} u (x) d x

,

ξ' \in ℝ^{k}

, k < n. We prove that for some s,s' the space

H^{s, s'}_k

is a multiplicative algebra.

Keywords

multiplicative algebra, Littlewood double decomposition

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