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Unit 6: Minkowski Inequalities
6.4 Review Questions Notes
1. If f, g are square integrable in the Lebesgue sense, prove that f + g is also square integrable
and
f + g f + g .
2 2 2
2. If | < p < , then show that equality can be true, iff there are non-negative constants and
, such that f = g.
6.5 Further Readings
Books Books: Stein, Elias (1970). Singular Integrals and Differentiability Properties of
Functions. Princeton University Press.
Hardy, G.H.; Littlewood, J.E.; Polya, G. (1952). Inequalities, Cambridge
Mathematical Library (second ed.). Cambridge: Cambridge University Press.
Online links Mathworld.wolfram.com>Calculus and Analysis>Inequalities
Planet math.org/Minkowski In-equality.html
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