Aliasing Error of Sampling Theorem

Let f∈Lpr（R）,1【p【∞,r∈N),the bound for aliasing of function fin Lp—metricesis given in[1].From embedding Theorem and Stein inequality,it follows,that if f∈Lpr（R）,1【p【∞,then f∈Lqr（R）,1【p【q≤∞ and f（k）∈Lp（R）∩Lq（R）,k=0,1,…,r-1.In this paper,we con-tinued Fang’s work in[1],and obtain the bound for aliasing error of function f∈Lpr（R）,1【p【∞,inLq-metrices（p≤q≤∞）.And the order is exact when 1【p≤q≤2.

Let f∈ Lpr( R), 1 < p < ∞ , r∈N), the bound for aliasing error of function fin Lp-metrices is given in [ 1 ]. From embedding Theorem and Stein inequality, it follows, that if f∈LPr(R) ,1<p < ∞ , then f∈Lqr(R),1<p<q≤∞ and f(k)∈Lp(R)∩Lq(R), k=0,1,…,r - 1. In this paper,we con-tinued Fang's work in [ 1 ], and obtain the bound for aliasing error of function f∈Lpr(R),1<p<∞, in Lq-metrices (p≤q≤∞ ). And the order is exact when 1 < p ≤ q ≤2.