Abstract. We give new sufficient conditions on absolutely continuous functions on ${\msbm R}^2$ to be multipliers of double Fourier transforms on $L^1({\msbm R}^2)$. Analogously, we give new sufficient conditions on double sequences of bounded variation to be multipliers of double Fourier series on $L^1({\msbm T}^2)$. We deal not only with even, but odd and even-odd functions and sequences, respectively. Our proofs rely on integrability results obtained recently.

AMS Subject Classification (1991): 42A45, 46A19

Keyword(s): Fourier transform, absolutely continuous function, Fourier series, Lebesgue integrability, sequence of bounded variation, multiplier, bounded linear operator, convolution

Received February 2, 1993. (Registered under 5551/2009.)