Delmonico, Cedric2010-11-302010-11-302010-11-30200810.1017/S1446788708000669https://infoscience.epfl.ch/handle/20.500.14299/60942WOS:000260072800004Let 1 < p < infinity, let G and H be locally compact groups and let c) be a continuous homomorphism of G into H. We prove, if G is amenable, the existence of a linear contraction of the Banach algebra CVp (G) of the p-convolution operators on G into CVp (H) which extends the usual definition of the image of a bounded measure by omega. We also discuss the uniqueness of this linear contraction onto important subalgebras of CVp(G). Even if G and H are abelian, we obtain new results. Let G(d) denote the group G provided with a discrete topology. As a corollary, we obtain, for every discrete measure, vertical bar parallel to mu vertical bar parallel to CVp(G) <= vertical bar parallel to mu vertical bar parallel to CVp(G(d)), for G(d) amenable. For arbitrary G, we also obtain vertical bar parallel to mu vertical bar parallel to CVp(G(d)) <= vertical bar parallel to mu vertical bar parallel to CVp(G). These inequalities were already known for p = 2. The proofs presented in this paper avoid the use of the Hilbertian techniques which are not applicable to p :A 2. Finally, for Gd amenable, we construct a natural map of CVp(G) into CVp (G(d)).convolution operatorspseudomeasuresp-multiplierstransform theoremHerz algebraMultipliersSubgroupstext::journal::journal article::research article