Nettet25. okt. 2015 · 1 Although these inequalities occur in various settings, and I have used them to complete a number of proofs, I can not say that I intuitively understand what their significance is. Holder's Inequality: Given p, q > 1 and 1 p + 1 q = 1, and ( x 1, …, x n), ( y 1, …, y n) ∈ R n or C n. http://www2.math.uu.se/~rosko894/teaching/Part_03_Lp%20spaces_ver_1.0.pdf
L Spaces - stat.cmu.edu
Nettet2. jul. 2024 · In the Holder inequality, we have ∑ x i y i ≤ ( ∑ x i p) 1 p ( ∑ y i q) 1 q, where 1 p + 1 q = 1, p, q > 1. In Cauchy inequality (i.e., p = q = 2 ), I know that the …Nettet25. okt. 2015 · I'd appreciate any insight into what these inequalities are measuring. Yes, Cauchy-Schwarz is Holder with p = q = 1 2. It says the dot product is at most the … jbg 203
a question about $L^p$ space and Holder inequality
NettetHolder's inequality. Suppose that f and g are two non negative real valued functions defined on a measure space ( X, μ). Let 0 < p < ∞. Holder's inequality says that ∫ f g d … Nettet19. nov. 2015 · Holder's inequality is a very general result concerning very general integrals in an arbitrary measure space. This is probably the most remarkable thing about Holder's inequality, and why it is so useful. Even in the statement of the theorem (as stated in the wikipedia link) the result only requires that we have a measure space ( S, … Nettet14. mar. 2024 · The inequality comes from the convexity of x p and probability measure d μ = g q d x.) In any Banach space V there is an inequality x, f ≤ ‖ x ‖ V ‖ f ‖ V ∗. This is almost a triviality, but it is a reflection of the geometrical fact that unit balls are convex. jbg 1 cd