Marian Vâjâitu: On the $C_p$-Banach algebra of the $r$-Lipschitz functions, p.293-301

Abstract:

Given a prime number $p$, we study the $C_p$-Banach algebra of the $r$-Lipschitz functions defined on compact subsets of $C_p$ by introducing a new seminorm on this space. Also, we give an estimation of the integral of a $r$-Lipschitz function with respect to a $s$-distribution and then we obtain a analogous of H$\rm\ddot{o}$lder's inequality.

Key Words: Lipschitz functions, local fields, distributions.

2000 Mathematics Subject Classification: Primary: 11S99;
Secondary: 11S80.

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