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

JOURNAL OF APPROXIMATION THEORY

卷:162

Article

Levis, Fabian E.

关键词: Orlicz-Lorentz spaces;    Maximal functions;    Best constant approximant;    a.e. convergence;   

DOI  :  10.1016/j.jat.2009.04.005

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free