Sobolev-Slobodetskii spaces

Vladimir B. Vasil’ev
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Vladimir B. Vasil’ev: Novgorod State University, Department of Mathematical Analysis

Chapter Chapter 3 in Wave Factorization of Elliptic Symbols: Theory and Applications, 2000, pp 13-17 from Springer

Abstract: Abstract Let s be an arbitrary real number. By definition the Sobolev-Slobodetskii space H s (ℝ m ) consists of distributions u for which their Fourier transforms are locally integrable functions ũ(ξ)such that 3.1.1 $$ \left\| u \right\|_s^2 = {\int\limits_{{\mathbb{R}^m}} {\left| {\mu \left( \xi \right)} \right|} ^2}{\left( {1 + \left| \xi \right|} \right)^{2s}}d\xi

Keywords: Compact Support; Integrable Function; Differentiable Function; Convex Cone; Restriction Operator (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-94-015-9448-6_3

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