We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φU * f(y) = f (y) almost everywhere for any function f in the space (LP, l∞)(G) (hence in LP(G)), 2 ≤ p ≤ ∞, where {φU} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q.
@article{urn:eudml:doc:41524,
title = {Pointwise convergence of the Fourier transform on locally compact abelian groups.},
journal = {Publicacions Matem\`atiques},
volume = {37},
year = {1993},
pages = {45-55},
mrnumber = {MR1240921},
zbl = {0817.43001},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41524}
}
Torres de Squire, María L. Pointwise convergence of the Fourier transform on locally compact abelian groups.. Publicacions Matemàtiques, Tome 37 (1993) pp. 45-55. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41524/