Cesàro Summability of Hardy Spaces on the Ring of Integers in a Local Field

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let O be the ring of integers in a local field K. We solve an open problem due to M. H. Taibleson (1975, "Math. Notes," Vol. 15, Princeton Univ. Press, Princeton, NJ): Suppose f∈L 1(O). Does the Cesàro means of f converge to f almost everywhere if K has characteristic zero? To this end we study the (H p,L p) boundedness of the associated maximal operator σ∥ to get the corresponding interpolation result on Hardy-Lorentz spaces; in particular we obtain that σ∥ is of weak type (1,1). The proof mainly depends on certain estimates for the oscillatory Dirichlet kernels, which are refinements of those obtained earlier by the author (1997, J. Math. Anal. Appl.208, 528-552).

Original languageAmerican English
Pages (from-to)626-651
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Volume249
Issue number2
DOIs
StatePublished - Sep 15 2000

Disciplines

  • Mathematics

Keywords

  • Atomic Hardy spaces
  • Cesàro means
  • Interpolation
  • Local field

Fingerprint

Dive into the research topics of 'Cesàro Summability of Hardy Spaces on the Ring of Integers in a Local Field'. Together they form a unique fingerprint.

Cite this