Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1969 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hörmander, L. (1969). Some special spaces of distributions. In: Linear Partial Differential Operators. Die Grundlehren der mathematischen Wissenschaften, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30722-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-30722-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-30653-6
Online ISBN: 978-3-662-30722-9
eBook Packages: Springer Book Archive