English

Boundedness of averaging operators on geometrically doubling metric spaces

Classical Analysis and ODEs 2018-12-06 v2

Abstract

We prove that averaging operators are uniformly bounded on L1L^1 for all geometrically doubling metric measure spaces, with bounds independent of the measure. From this result, the L1L^1 convergence of averages as r0r \to 0 immediately follows.

Keywords

Cite

@article{arxiv.1710.04233,
  title  = {Boundedness of averaging operators on geometrically doubling metric spaces},
  author = {J. M. Aldaz},
  journal= {arXiv preprint arXiv:1710.04233},
  year   = {2018}
}

Comments

7 pages, to appear in Ann. Acad. Sci. Fenn. Math