Dimension-free estimates for the vector-valued variational operators

Abstract

In this paper, We study dimension-free $L^p$ estimates for UMD lattice-valued $q$-variations of Hardy-Littlewood averaging operators associated with the Euclidean balls.

References in corpus (5)

• Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
• Weighted variation inequalities for differential operators and singular integrals in higher dimensions
• Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs
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• Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in ${\mathbb{Z}}^d$