Weighted variation inequalities for differential operators and singular integrals in higher dimensions

Abstract

We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.

References in corpus (4)

• Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
• Weighted and vector-valued variational estimates for ergodic averages
• Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs
• Vector valued $q$-variation for differential operators and semigroups I

Cited by in corpus (12)

• Weighted and vector-valued variational estimates for ergodic averages
• Sparse domination of sharp variational truncations
• Variational inequalities for the commutators of rough operators with BMO functions
• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• Variational truncations of singular integrals on spaces of homogeneous type
• Variational characterizations of weighted Hardy spaces and weighted $BMO$ spaces
• Variation operators for semigroups associated with Fourier-Bessel expansions
• Vector-valued $q$-variational inequalities for averaging operators and Hilbert transform
• On the compactness of oscillation and variation of commutators
• Dimension-free estimates for the vector-valued variational operators
• Variational Inequalities for Bilinear Averaging Operators over Convex Bodies
• Sparse dominations and weighted variation inequalities for singular integrals and commutators