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The Multipliers for Lp(G)

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 175)

Abstract

In this chapter we shall investigate the multipliers for the pair (L p (G), L p (G)). We have proven some scattered results pertaining to M(L p (G)) in the previous chapters. In particular, we have already discussed to some extent the cases when p =1 and p = ∞. Consequently we shall now restrict our attention primarily to the values of p such that 1< p < ∞. We shall show in the following sections that the multipliers for L p (G) can, in a certain sense, be represented either as multiplication of the Fourier transform by a bounded function or as a convolution operator, in this instance convolution with a pseudomeasure. We shall also investigate the relationships between the spaces M(L p (G)) for various values of p, obtain some results on the existence of bounded functions which do not determine multipliers for L p (G), and examine the notion of the derived space for L p (G). As usual we shall consider only the commutative case.

Keywords

Banach Algebra Proper Subset Measurable Subset Compact Abelian Group Algebra Isomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  1. 1.Department of MathematicsWesleyan UniversityMiddletownUSA

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