Fourier Transformation of Lploc-functions

In this paper, we study the Fourier transformation of Lploc-functions and Lqc-functions. Here we assume that the condition 1/p+1/q=1, (1 ≤ p ≤ ∞, 1 ≤ q ≤ ∞) is satisfied. Thereby we prove the structure theorems of the image spaces FLploc and FLqc. We study the convolution f∗g of a Lrc-function f and a Lploc-function g. Here assume d ≥ 1. Further we assume that the condition 1/q=1/p+1/r−1, (1 ≤ p ≤ ∞, 1 ≤ q ≤ ∞, 1 ≤ r ≤ ∞) is satisfied. This is a generalization of the theory of Fourier transformations of L2loc-functions.