ON CONVOLUTION-OPERATORS AND MULTIPLIERS OF DISTRIBUTIONS OF LP-GROWTH

[摘要] We consider the spaces of convolution operators and multipliers of the spaces D(Lp)' 1 less-than-or-equal-to P < infinity, of distributions of L(p)-growth. We characterize the space O(c,p)' of convolution operators and provide it with a natural topology. It turns out that the space D(L1)' is continuously embedded in O(c,p)' for all p in [1, infinity). We define O(m,q), 1/p + 1/q = 1, the space of multipliers of D(Lp)', and provide it with natural topologies, and then show that the topological spaces O(m,q) and D(Linfinity) coincide. (C) 1994 Academic Press, Inc.

[发布日期] 1994-04-01