Maximal Inequalities and Lebesgue's Differentiation Theorem for Best Approximant by Constant over Balls |
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Authors: | Fernando Mazzone Hctor Cuenya |
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Institution: | Departamento de Matemática, Facultad de Cs. Exactas Fco-Qcas y Naturales, Universidad Nacional de Río Cuarto, (5800), Río Cuarto, Argentina |
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Abstract: | For fLp(
n), with 1p<∞, >0 and x
n we denote by T(f)(x) the set of every best constant approximant to f in the ball B(x, ). In this paper we extend the operators Tp to the space Lp−1(
n)+L∞(
n), where L0 is the set of every measurable functions finite almost everywhere. Moreover we consider the maximal operators associated to the operators Tp and we prove maximal inequalities for them. As a consequence of these inequalities we obtain a generalization of Lebesgue's Differentiation Theorem. |
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Keywords: | best approximant maximal inequalities a e convergence |
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