| Abstract: | In this paper, we consider a family of finite difference operators {Ah }h >0 on discrete L q ‐spaces L q (?N h ). We show that the solution u h to u ′h (t) – A h u h(t) = f h (t), t > 0, u h (0) = 0 satisfies the estimate ‖A h u h ‖equation/tex2gif-inf-15.gif ≤ C ‖f h ‖equation/tex2gif-inf-21.gif, where C is independent of h and f h . In this case, the family {A h }h >0 is said to have discrete maximal L p regularity on the discrete L q ‐space. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
