JACKSON THEOREMS FOR ERDOS WEIGHTS IN L-P (0-LESS-THAN-P-LESS-THAN-OR-EQUAL-TO-INFINITY)

An Erdos weight is of the form TY:=e(-Q) where Q is even and of faster than polynomial growth at infinity. For example, we can take Q(x):=ex p(k)([X](alpha)), k greater-than-or-equal-to 1, alpha greater-than 0, x is an element of R, where exp(k) denotes the kth iterated exponentia l. We prove Jackson theorems in weighted L-p spaces with norm parallel to f W parallel-to (Lp(R)) for all 0 less-than p less-than-or-equal-t o infinity. These are the first proper Jackson theorems for Erdos weig hts even in L-infinity. An interesting feature is a Timan-Nikolskii-Br udnyi effect: The degree of approximation improves towards the endpoin ts of a certain interval. By contrast, there is no such feature for Fr eud weights. (C) 1998 Academic Press.