ON L(P)-MULTIPLIERS OF MIXED-NORM TYPE

[摘要] Given a sequence (g(n)) of Fourier multipliers for L(p)(R), 1 p < infinity, let g := SIGMA(infinity)infinity g(n)CHI(n), where CHI(n) denotes the characteristic function of the interval [2n, 2n+1] in R. Assuming (g(n)) is-an-element-of l(s)(M(p)) for some s with 0 < s less-than-or-equal-to infinity, we determine the values of s for which g is, or is not, a multiplier of L(p)(R). Our results sharpen a result of Littman et al. who, in 1968, considered the case when s = infinity. The same problem is also considered for multipliers in L(p)-spaces defined on a locally compact Vilenkin group. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-15