Homogeneous distributions in $\mathcal D'_{L^q}$


S. Pilipović, D. Rakić, N. Teofanov




We study the homogeneity property on a scale of subspaces $\mathcal D_{L^q}(\mathbb R^n)$, $1\leq q\infty x$ of the space of tempered distributions $\mathcal S'(\mathbb R^n)$. It is shown that a homogeneous distributions belong to $\mathcal D'_{L^q}(R^n)$ if and only if its degree of homogeneity belongs to $(—\infty,-\frac nq)$, $1\leq q\leq\infty$ (if $q=\infty$, then $\frac nq=0$).