Abstract
Let 1≦p≦∞, and denote by J p J P(R) the set of tempered distributions u on the real line R such that the transformation ̅→u* ̅, defined initially for infinitely differentiable ̅ with compact support, extends to a bounded linear operator (which we shall denote by [u]) from L P(R) to L P(R) (this for p>∞; for P = ∞, the closure of the set of test functions ̅ is of course the set of continuous functions *) in L∞ (R).)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
J. A. Clarkson, Uniformly Convex Space. Trans. Amer. Math. Soc. 40 (1936), 396–414.
L. Hörmander, Estimates for translation invariant operators in Lp spaces. Acta Math. 104 (1960), 93–140.
K. de Leeuw, On L p multipliers. Ann. of Math. 81 (1965), 364–379.
E. Lukäcs, Characteristic Functions. Griffin, London 1960.
H. S. Shapiro, Topics in Approximation Theory. Lecture Notes in Math. 187 Springer, Berlin 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Shapiro, H.S. (1972). Fourier Multipliers whose Multiplier Norm is an Attained Value. In: Butzer, P.L., Kahane, JP., Szökefalvi-Nagy, B. (eds) Linear Operators and Approximation / Lineare Operatoren und Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7283-6_30
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7283-6_30
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7285-0
Online ISBN: 978-3-0348-7283-6
eBook Packages: Springer Book Archive