When the cone condition fails |
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Authors: | Michel Weber |
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Institution: | (1) Mathématique (IRMA) Université Louis-Pasteur et C.N.R.S., 7 Rue René Descartes, 67084 Strasbourg, Cedex, France |
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Abstract: | Summary We study the class of convergence E∪L1of a family of moving averages which does not satisfy the cone condition. We show that if E0is a finite subset of Ewhich is (E)-stable for the multiplication operation: f,g∈E0 →f·g∈E, then the supremum sup { f, f∈E0} is dominated by sup{ g, g∈G0}where G0is a Gaussian family with same covariance function. This is used to derive a maximal inequality for families Fsuch that each finite subset is E-stable and Fis a GB set. |
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