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Abstract. Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we give a notion of complementary spaces for Fourier transforms treated as distributions. Applications to multipliers and summability are given. Some known conditions turn out to be effective for $(L^p,L^p)$ multipliers with $1 \le p \le\infty $.
AMS Subject Classification
(1991): 42A38, 42A24, 42A45
Keyword(s):
Fourier transform,
complementary space,
summability,
multiplier
Received September 9, 1994 and in revised form January 13, 1995. (Registered under 5618/2009.)
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