Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
2 Downloads (Pure)

Abstract

Let X be a Banach function space over the unit circle T and let H[X] be the abstract Hardy space built upon X. If the Riesz projection P is bounded on X and a ∈ L, then the Toeplitz operator Taf = P(af) is bounded on H[X]. We extend well-known results by Brown and Halmos for X = L2 and show that, under certain assumptions on the space X, the Toeplitz operator Ta is bounded (resp., compact) if and only if a ∈ L (resp., a = 0). Moreover, ||a||L ≤ ||Ta||ℬ(H[X]) ≤ ||P||ℬ(X)||a||L . These results are specified to the cases of abstract Hardy spaces built upon Lebesgue spaces with Muckenhoupt weights and Nakano spaces with radial oscillating weights.

Original languageEnglish
Article number9768210
JournalJournal of Function Spaces
Volume2017
DOIs
Publication statusPublished - 2017

Keywords

  • REARRANGEMENT-INVARIANT SPACES
  • OSCILLATING WEIGHTS
  • NORM

Fingerprint Dive into the research topics of 'Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces'. Together they form a unique fingerprint.

Cite this