1. As Prof. Hans G. Feichtinger poinyed the proof for the first question is essentially working with continuous functions with compact support and then using the fact that such functions are dense in L^1. Infact the very same proof also works for any L^p, p finite.
2. Apart from Prof. Hans G. Feichtinger's description on multipliers they are equivalently described as those continuous functions from L^p to L^p that commute with translations. Well, refarding the books one can look into the book by "sadosky" on "Interpolation of operators and singular integrals". In fact the theory of multipliers can be extended to a Locally Compact Group. For details into the book be "Introduction to Multipliers" by "Larsen".
3. As for as the definition of the Fourier Algebra is concerned Reiter's book on "Classical Harmonic analysis and Locally Compact Groups" is concerned the best. In fact there is a paper by Eymard on fourier algebra for a general locally compact group which is a frech paper, while the Reiter's books deals only with the Abelian case.

From: fatima22_m <fatima22_m@...>
Subject: [harmonic] find someone to ask question
To: harmonicanalysis@yahoogroups.com
Date: Saturday, 27 September, 2008, 7:05 AM

dear memebers
here there are questions
1-how we can prove that translation in L^1(G) is norm continuouse?
2- what is L_(P) multiplier theory do you have refrences for a
begginer?
3-what is the exact definition of fourier algebra?
best wishes
fatima