On Convolution Operators and Multipliers of Distributions of Lp-Growth

We consider the spaces of convolution operators and multipliers of the spaces D′Lp, 1 ≤ P < ∞, of distributions of Lp-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, ∞). We define Om,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 Om,q and DL∞ coincide.