Abstract
Let r > 0 be a fixed number and let \( \mathcal{U} \) be a domain in ℝn containing a closed ball of radius r. Denote by V r \( \mathcal{U} \) the set of functions f ∈ L loc \( \mathcal{U} \) with zero averages over all closed balls of radius r lying in \( \mathcal{U} \). For s ∈ ℕ+ or s = ∞ we set \( V_r^s \left( \mathcal{U} \right) = \left( {V_r \cap C^s } \right)\left( \mathcal{U} \right) \).
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© 2003 Springer Science+Business Media Dordrecht
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Volchkov, V.V. (2003). Functions with Zero Averages Over Balls on Subsets of the Space ℝn . In: Integral Geometry and Convolution Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0023-9_10
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DOI: https://doi.org/10.1007/978-94-010-0023-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3999-4
Online ISBN: 978-94-010-0023-9
eBook Packages: Springer Book Archive