Some special spaces of distributions

  • Lars Hörmander
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 ϵ L P . The set of all such temperate distributions u is denoted by B p, k here. Only the cases p = 2, p = ∞ and p = 1 are really interesting.


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

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • Lars Hörmander
    • 1
  1. 1.University of LundSweden

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