Maximal Inequalities and Lebesgue's Differentiation Theorem for Best Approximant by Constant over Balls
For f∈Lp(Rn), with 1⩽p0 and x∈Rn we denote by Tε(f)(x) the set of every best constant approximant to f in the ball B(x, ε). In this paper we extend the operators Tεp to the space Lp−1(Rn)+L∞(Rn), where L0 is the set of every measurable functions finite almost everywhere. Moreover we consider the max...
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| Veröffentlicht in: | Journal of approximation theory 2001-06, Vol.110 (2), p.171-179 |
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| container_title | Journal of approximation theory |
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| creator | Mazzone, Fernando Cuenya, Héctor |
| description | For f∈Lp(Rn), with 1⩽p0 and x∈Rn we denote by Tε(f)(x) the set of every best constant approximant to f in the ball B(x, ε). In this paper we extend the operators Tεp to the space Lp−1(Rn)+L∞(Rn), where L0 is the set of every measurable functions finite almost everywhere. Moreover we consider the maximal operators associated to the operators Tεp and we prove maximal inequalities for them. As a consequence of these inequalities we obtain a generalization of Lebesgue's Differentiation Theorem. |
| doi_str_mv | 10.1006/jath.2001.3559 |
| format | Article |
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| source | Access via ScienceDirect (Elsevier); EZB-FREE-00999 freely available EZB journals |
| subjects | best approximant maximal inequalities, a.e. convergence |
| title | Maximal Inequalities and Lebesgue's Differentiation Theorem for Best Approximant by Constant over Balls |
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