Some special spaces of distributions
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 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.
KeywordsCompact Subset Cauchy Sequence Local Space Special Space Linear Partial Differential Operator
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