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Tagged with bounds-of-integration inequality
3
questions
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Upper bound of the integral $\int_\delta^\infty t^m e^{-\nu t^2} dt$
I am reading Wong's book on "Asymptotic Approximations of Integrals". On page 497, the book recalls (without proof) the following estimate: for all $\delta>0$ and $\nu>1$,
$$
\int_\...
- 13.3k
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Show that the sum of two integrals is finite.
How to easy show that
\begin{equation} \int_0^1 \frac{1-e^{-x}}{x}dx+\int_1^M\frac{-e^{-x}}{x}dx \end{equation} is less than finite number?
- 31
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HLS inequality not suitable to bound this integral
I am trying to bound the following integral for $f \in L^{n/2}(\mathbb{R}^n)$:
$\int_{\mathbb{R}^n}\int_{\mathbb{R}^n} f(x) \lvert x-y \lvert^{2(2-n)}f(y)dxdy$. Because of the factor 2 in the exponent,...
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