A remark on a paper of F. Chiarenza and M. Frasca

In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of $\mathrm{\mid }bu{\mathrm{\mid }}^p$ through the integral of $\mathrm{\mid }Du{\mathrm{\mid }}^p$ for $p>1$. Formally their proof is valid only for $d\ge 3$. We present here further generalization with a different proof in which $D$ is replaced with the fractional power of the Laplacian for any dimension $d\ge 1$.