Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 497-503

BOUNDEDNESS OF AVERAGING OPERATORS ON GEOMETRICALLY DOUBLING METRIC SPACES

Jesús M. Aldaz

Universidad Autónoma de Madrid, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departamento de Matemáticas
Cantoblanco 28049, Madrid, Spain; jesus.munarriz 'at' uam.es

Abstract. We prove that averaging operators are uniformly bounded on L^p for all geometrically doubling metric measure spaces and all 1 ≤ p < ∞, with bounds independent of the measure. From this result, the L^p convergence of averages as r → 0 immediately follows.

2010 Mathematics Subject Classification: Primary 41A35.

Key words: Averaging operators, goemetrically doubling metric spaces.

Reference to this article: J. M. Aldaz: Boundedness of averaging operators on geometrically doubling metric spaces. Ann. Acad. Sci. Fenn. Math. 44 (2019), 497-503.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4430