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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.

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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

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