We prove the existence of nontrivial functions in ℝn, n ≥ 2, with vanishing integrals over balls of fixed radius and given majorant of growth.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 857–861, June, 2008.
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Ochakovskaya, O.A. Majorants of functions with vanishing integrals over balls. Ukr Math J 60, 1003–1008 (2008). https://doi.org/10.1007/s11253-008-0098-4
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DOI: https://doi.org/10.1007/s11253-008-0098-4