Weak inequalities for maximal functions in Orlicz-Lorentz spaces and applications

作者：Levis Fabian E^*

来源：Journal of Approximation Theory, 2010, 162(2): 239-251.

DOI：10.1016/j.jat.2009.04.005

• Orlicz-Lorentz spaces
• Maximal functions
• Best constant approximant
• a.e. convergence

Let 0 < alpha <= infinity and let {B(x, epsilon)}(epsilon), epsilon > 0, denote a net of intervals of the form (x - epsilon, x + epsilon) subset of vertical bar 0, alpha). Let f(epsilon)(x) be any best constant approxi mation of f is an element of Lambda(m,phi') on B (x, epsilon). Weak inequalities for maximal functions associated with {f(epsilon)(x)}(epsilon), in Orlicz-Lorentz spaces, are proved. As a consequence of these inequalities we obtain a generalization of Lebesgue's Differentiation Theorem and the pointwise convergence of f(epsilon)(x) to f(x), as epsilon -> 0.

• 出版日期2010-2