Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a generalization of the Cauchy-Schwarz Inequality for multiple integrals?

share|improve this question
4  
You mean like $|\iint f\overline g|\leq\sqrt{\iint|f|^2}\sqrt{\iint|g|^2}$ on subsets of $\mathbb{R}^2$, and higher dimensional analogues? If so, then yes, these are all special cases of the Cauchy-Schwarz inequality: en.wikipedia.org/wiki/Cauchy-schwarz –  Jonas Meyer Apr 4 '11 at 0:12

1 Answer 1

According to Michael Steele, one generalization is the following for double integrals: $S \subset \mathbb{R}^2, f: S \to \mathbb{R}$ and $g: S \to \mathbb{R}$, then $$A = \iint_{S} f^{2} \ dx \ dy, \ B = \iint_{S} fg \ dx \ dy, \ C = \iint_{S} g^{2} \ dx \ dy$$ satisfy $|B| \leq \sqrt{A} \cdot \sqrt{C}$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.