Hello,

When I read Stein's book of Singular Integrals, at p. 118, there is an obvious mistake:

$$ \int_{R^n} |x-y|^{-n+\alpha} |y|^{-n+\beta}=\frac{\gamma(\alpha)\gamma(\beta)}{\gamma(\alpha+\beta)},\quad 0<\alpha, 0<\beta, $$ with $\alpha+\beta < n$ and $$ \gamma(a) = \pi^{n/2} 2^a \frac{\Gamma(a/2)}{\Gamma((n-a)/2)}. $$

Clearly, in one dimensional case, $$ \int_{0}^1 |1-y|^{-1+\alpha} |y|^{-1+\beta}=\frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)},\quad 0<\alpha, 0<\beta, $$ with $\alpha+\beta < 1$;see wikipedia. However, $$ \int_{R^1} |1-y|^{-1+\alpha} |y|^{-1+\beta}= \infty. $$ So we need properly reduce the integral domain from $R^n$ to some balls. Does anyone know this correct integration domain?

Thank you very much!

Anand

EDIT:

(1) Whether does any one know an online errata of this book?