MathLiveHölder's inequality
It bounds the integral of the product of two functions by the product of their Lp norms, where p and q are conjugate exponents. It is used throughout analysis to estimate integrals and to show that certain function spaces are well behaved.
\|fg\|_1 \le \|f\|_p \|g\|_qWhat the symbols mean
| a measurable function | |
| a measurable function | |
| the L1 norm of the product fg, i.e. the integral of |fg| | |
| the L^p norm of f | |
| the L^q norm of g | |
| an exponent with 1 \le p \le \infty | |
| the conjugate exponent of p, satisfying 1/p + 1/q = 1 |
About this formula
- FieldMathematics
- TopicFunctional analysis
- LevelUniversity
- Also calledintegral Holder inequality, Lp spaces inequality, conjugate exponents inequality, L1 norm of product bound, Holder's inequality for integrals
- SourceWikidata Q731894
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “hölder's inequality”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.