Abstract. Strong summability results are proved for $d$-dimensional Fourier transforms of $f\in L_p(\log L)^{d-1}({\msbm R}^d)$ and $f\in L_p({\msbm R}^d)$.

AMS Subject Classification (1991): 42B08, 42A24, 42A38

Keyword(s): Fourier transforms, strong summability, \theta, -summability, strong maximal function, Lebesgue points

Received March 29, 2007, and in revised form May 21, 2007. (Registered under 6012/2009.)