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Published online by Cambridge University Press: 22 February 2019
Chapter2 covers the foundational inequalities for integrals of functions in Euclidean space. The two key results in this chapter are that symmetric decreasing rearrangement of a continuous function decreases the modulus of continuity, and that certain integral expressions increase when functions are replaced by their symmetric decreasing rearrangement. Other results include the Hardy-Littlewood inequalityand the contractivity of rearrangements in the L-infinity norm.
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