On dimension-free variational inequalities for averaging operators in mathbb R^d

Jean Bourgain , Mariusz Mirek , Elias M. Stein , B{\l}a\.zej Wr\'obel

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keywords averagingdimension-freeinequalitiesmathbboperatorsbodiesconvexdefined

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We study dimension-free $L^p$ inequalities for $r$-variations of the Hardy--Littlewood averaging operators defined over symmetric convex bodies in $\mathbb R^d$.

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On dimension-free variational inequalities for averaging operators in mathbb R^d

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