ソボレフ乗数の理論：微分演算子と積分演算子への応用 Theory of Sobolev Multipliers : With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften) 〈Vol. 337〉

Maz'ya, Vladimir G./ Shaposhnikova, Tatiana O.

Springer（2008/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 614 p.／サイズ 2 illus.
• 商品コード 9783540694908

基本説明

乗数に関する理論を包括的に解説する。

Full Description

'I never heard of "Ugli?cation," Alice ventured to say. 'What is it?" Lewis Carroll, "Alice in Wonderland" Subject and motivation. The present book is devoted to a theory of m- tipliers in spaces of di?erentiable functions and its applications to analysis, partial di?erential and integral equations. By a multiplier acting from one functionspaceS intoanotherS ,wemeanafunctionwhichde?nesabounded 1 2 linear mapping ofS intoS by pointwise multiplication. Thus with any pair 1 2 of spacesS ,S we associate a third one, the space of multipliersM(S?S ) 1 2 1 2 endowed with the norm of the operator of multiplication. In what follows, the role of the spacesS andS is played by Sobolev spaces, Bessel potential 1 2 spaces, Besov spaces, and the like. The Fourier multipliers are not dealt with in this book. In order to emp- size the di?erence between them and the multipliers under consideration, we attach Sobolev's name to the latter. By coining the term Sobolev multipliers we just hint at various spaces of di?erentiable functions of Sobolev's type, being fully aware that Sobolev never worked on multipliers. After all, Fourier never did either.