JUMPS OF DISTRIBUTIONS IN $Z^{\prime}$ AND LIZORKIN SPACES

Source abstract

In this paper, we give some results in the space $Z^{\prime}$ and the space of Lizorkin distributions. We study the local jump behavior of distributions through their analytic representations in the upper and lower half-planes, and establish an asymptotic formula connecting the jumps with the boundary behavior of $G$ and its derivatives. Also, we find the jump in terms of a series. The proof is based on the decomposition of the Fourier transform into components supported on the positive and negative half lines and on the associated analytic representations.