Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 119-133

AVERAGING ON n-DIMENSIONAL RECTANGLES

Emma D'Aniello and Laurent Moonens

Seconda Università degli Studi di Napoli, Scuola Politecnica e delle Scienze di Base, Dipartimento di Matematica e Fisica
Viale Lincoln n. 5, 81100 Caserta, Italia; emma.daniello 'at' unina2.it

Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, CNRS UMR8628
Université Paris-Saclay, Bâtiment 425
F-91405 Orsay Cedex, France; laurent.moonens 'at' math.u-psud.fr

Abstract. In this work we investigate families of translation invariant differentiation bases B of rectangles in Rⁿ, for which L log^n-1L(Rⁿ) is the largest Orlicz space that B differentiates. In particular, we improve on techniques developed by Stokolos in [11] and [13].

2010 Mathematics Subject Classification: Primary 42B25; Secondary 26B05.

Key words: Maximal functions and operators, differentiation bases, Lebesgue's differentiation theorem.

Reference to this article: E. D'Aniello and L. Moonens: Averaging on n-dimensional rectangles. Ann. Acad. Sci. Fenn. Math. 42 (2017), 119-133.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4207