BOUNDEDNESS OF g-FUNCTIONS ON TRIEBEL-LIZORKIN SPACES

We prove that the $g$-function operator $g_\phi$, where $\phi(x)=h(|x|)\Omega(x)$ with $\Omega(x)=\Omega(x')\in H^1(S^{n-1})$ and $h(s)$ satisfing certain continuity hypothesis, is bounded on Triebel-Lizorkin space $F^{\alpha,q}_p(R^n)$ when $0<\alpha<1$ and $1