Transferring Fourier multipliers from $S\sp {2p-1}$ to $H\sp {p-1}$

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

1 p - adic Fourier theory

In the early sixties, Amice ([Am1], [Am2]) studied the space of K-valued, locally analytic functions on Z Z p and formulated a complete description of its dual, the ring of K-valued, locally Q p-analytic distributions on Z Z p , when K is a complete subfield of C p. She found an isomorphism between the ring of distributions and the space of global functions on a rigid variety over K parameteriz...

Mod (2p + 1)-Orientations and $K1,2p+1-Decompositions

In this paper, we established an equivalence between the contractible graphs with respect to the mod (2p + 1)-orientability and the graphs with K1,2p+1-decompositions. This is applied to disprove a conjecture proposed by Barat and Thomassen that every 4-edge-connected simple planar graph G with |E(G)| ≡ 0 (mod 3) has a claw-decomposition.

On mod (2p+1)-orientations of graphs

It is shown that every (2p+ 1) log2(|V (G)|)-edge-connected graph G has a mod (2p+ 1)orientation, and that a (4p+ 1)-regular graph G has a mod (2p+ 1)-orientation if and only if V (G) has a partition (V , V −) such that ∀U ⊆ V (G), |∂G(U)| ≥ (2p+ 1)||U ∩ V | − |U ∩ V −||. These extend former results by Da Silva and Dahad on nowhere zero 3-flows of 5-regular graphs, and by Lai and Zhang on highl...

Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1 < p < ∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.