Several Integral Estimates and Some Applications

Abstract

In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function space $F(p,\mu ,s)$ to the normal weight Bloch type space ${\mathcal{B}}_{\nu }(B_n)$ on the unit ball $B_n$ of ${\mathbb{C}}^n$, where $\mu$ and $\nu$ are two normal functions on $[0,1)$. For the special normal function $\mu (r)=(1-r^2{)}^{\alpha }{\log }^{\beta }\frac{e}{1-r^2}$ ($\alpha >0$, $-\infty <\beta <\infty$), the authors give the necessary and sufficient conditions of pointwise multipliers from $F(p,\mu ,s)$ to ${\mathcal{B}}_{\nu }(B_n)$ for all cases.