Take the 2-minute tour ×  Let $D$ be a compact in $\mathbb{R}^n$
and $f(x,y,z)$ be a function from $D \times D \times D$ to
$\mathbb{R}$ such that it has singularity if $x = y = z$ and it
is continuous otherwise. How to estimate the growth rate of
function $$ g(x,y) = \int\limits_{D} f(x,y,z) \, dz $$ in points
$x = y$? Give me some reference please.  share|improve this
question Do you mean $D\in \mathbb{R}$? Also, what do you mean
by the "grow(th) rate"? –  nbubis May 2 '12 at 8:48 @nbubis
$D\subseteq \mathbb{R}^n$. I mean I want to find such
$\alpha_1<0$ and $\alpha_2<0$ that $A_1|x-y|^{\alpha_1}
\leqslant |g(x,y)| \leqslant A_2|x-y|^{\alpha_3}$ in $D \times
D$ if they exist. –  Nimza May 2 '12 at 12:13 add comment   Your
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