A Lebesgue Type Differentiation Theorem for Best Approximations by Constant in Orlicz Spaces

S. FAVIER; F. ZÓ

REAL ANALYSIS EXCHANGE

Michigan State University Press

Lugar: Michigan; Año: 2005 vol. 30 p. 29 - 42

0147-1937

The best approximation operator by constants is extended from an Orlicz space L^{varphi} ( R^m) to the space L^{varphi ´} ( R^m), and it is proved some properties on this extended operator. Let f_{varepsilon}(x) be any best approximation of fin L^{varphi ´} (R^m) on a suitable subset B of  R^m.  Weak and strong inequalities are proved for the maximal function associated to the family {f_{varepsilon}(x)} which is used in the study of the pointwise convergence of  f_{varepsilon}(x) to f(x).