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In this thesis, we establish some ergodic theorems related to A p (G), the Figà-Talamanca-Herz algebra of a locally compact group G. This thesis is divided in two main portions. The rst part is primarily concerned with the study of ergodic sequences in A p (G) and with a newly introduced notion of ergodic multipliers. After presenting a full description of the non-degenerate * -representations of A p (G) and of their extensions to the multiplier algebra MA p (G), it is shown that, for alldoi:10.7939/r35g7w fatcat:3cznlllxmjdw5of4y5nzctu2li