L^p-multipliers of mixed-norm type on locally compact Vilenkin groups

C. W. Onneweer
Department of Mathematics
University of New Mexico
Albuquerque, NM 87131
USA
e-mail: onneweer@math.unm.edu
and
T. S. Quek
Department of Mathematics
National University of Singapore
Singapore 119260
Republic of Singapore
e-mail: matqts@leonis.nus.sg

Abstract:

Let G be a locally compact Vilenkin group with dual group $\Gamma$. We prove Littlewood-Paley type inequalities corresponding to arbitrary coset decompositions of $\Gamma$. These inequalities are then applied to obtain new L^p(G) multiplier theorems. The sharpness of some of these results is also discussed.

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