The Brown–Halmos theorem for a pair of abstract Hardy spaces

Alexei Karlovich, Eugene Shargorodsky

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let H[X] and H[Y] be abstract Hardy spaces built upon Banach function spaces X and Y over the unit circle T. We prove an analogue of the Brown–Halmos theorem for Toeplitz operators Ta acting from H[X] to H[Y] under the only assumption that the space X is separable and the Riesz projection P is bounded on the space Y. We specify our results to the case of variable Lebesgue spaces X=Lp(⋅) and Y=Lq(⋅) and to the case of Lorentz spaces X=Y=Lp,q(w), 1<p<∞, 1≤q<∞ with Muckenhoupt weights w∈Ap(T).

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - 2018

Keywords

  • Banach function space
  • Brown–Halmos theorem
  • Pointwise multiplier
  • Toeplitz operator
  • Variable Lebesgue space
  • Weighted Lorentz space

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