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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).)

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© 1972 Birkhäuser Verlag Basel

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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

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  • 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

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