Some special spaces of distributions

Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 116)


In an existence theory for partial differential equations it is important to give precise statements concerning the regularity of the solutions obtained. Now a condition on the regularity of a distribution or function u (with compact support) can also be regarded as a condition on the behavior at infinity of the Fourier transform û. To classify this behavior one may for example ask for which weight functions k it is true that kû ∈ L p . The set of all such temperate distributions u is denoted by p,k ,here. Only the cases þ = 2, þ = ∞ and þ = 1 are really interesting. Concerning k we shall make some assumptions (Definition 2.1.1) which ensure that p,k , is a module over C 0 and which are suggested by the theory developed in the following chapters.


Compact Subset Cauchy Sequence Local Space Special Space Linear Partial Differential Operator 
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Copyright information

© Springer-Verlag OHG, Berlin · Göttingen · Heidelberg 1963

Authors and Affiliations

  1. 1.University of Stockholm and at Stanford UniversitySweden

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