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Hölder's inequality
Inequality between integrals in Lp spaces
Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. The numbers p and q above are said to be Hölder conjugates of each other. The special case p = q = 2 {\displaystyle p=q=2} gives a form of the Cauchy–Schwarz inequality. Hölder's inequality holds even if ‖ f g ‖ 1 {\displaystyle \|fg\|_{1}} is infinite, the right-hand side also being infinite in that case. Conversely, if f is in L p ( μ ) {\displaystyle L^{p}(\mu )} and g is in L q ( μ )...
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