Exponential Squared Integrability of the Discrepancy Function in Two Dimensions

DOI10.1112/S0025579300000930zbMath1198.42001arXiv0810.5544OpenAlexW3100530683MaRDI QIDQ3400764

Dmitriy Bilyk, Armen Vagharshakyan, Ioannis Parissis, Michael T. Lacey

Publication date: 5 February 2010

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.5544

zbMATH Keywords

Littlewood-Paley inequalitydiscrepancy functionirregularities of distribution

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Irregularities of distribution, discrepancy (11K38)

Related Items (12)

BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension ⋮ Cyclic shifts of the van der Corput set ⋮ Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences ⋮ DISCREPANCY OF SECOND ORDER DIGITAL SEQUENCES IN FUNCTION SPACES WITH DOMINATING MIXED SMOOTHNESS ⋮ The BMO-discrepancy suffers from the curse of dimensionality ⋮ Discrepancy of Digital Sequences: New Results on a Classical QMC Topic ⋮ Fibonacci sets and symmetrization in discrepancy theory ⋮ Orlicz spaces bounds for special classes of hyperbolic sums ⋮ Tractability properties of the discrepancy in Orlicz norms ⋮ \(L_p\)- and \(S_{p, q}^r B\)-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases ⋮ Calculation of Discrepancy Measures and Applications ⋮ Proof techniques in quasi-Monte Carlo theory

Cites Work

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• On the small ball inequality in all dimensions
• On the small ball inequality in three dimensions
• On the discrepancy function in arbitrary dimension, close to \(L^1\)
• Some weighted norm inequalities concerning the Schrödinger operators
• Bounded double square functions
• Irregularities of distribution. I
• A continuous version of duality of \(H^ 1\) with BMO on the bidisc
• The small ball problem for the Brownian sheet
• An inequality for trigonometric polynomials and its application for estimating the entropy numbers
• The extreme and \(L^2\) discrepancies of some plane sets
• Multiparameter operators and sharp weighted inequalities
• Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains
• ON IRREGULARITIES OF DISTRIBUTION II
• Sharp Square-Function Inequalities for Conditionally Symmetric Martingales
• Metric entropy of the integration operator and small ball probabilities for the Brownian sheet
• BMO from dyadic BMO on the bidisc
• Geometric discrepancy. An illustrated guide

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