Bounded evaluation operators from H-p into l(q)

Martin, P Smith

Research output: Contribution to journalArticlepeer-review

Abstract

Given 0 < p, q < infinity and any sequence Z = {z(n)} in the unit disc D, we define an operator from functions on D to sequences by T-zp(f) = {(1-vertical bar zn vertical bar(2))(1/p)f(z(n))}. Necessary and sufficient conditions on {z(n)} are given such that T.,p maps the Hardy space H-p boundedly into the sequence space l(q) . A corresponding result for Bergman spaces is also stated.

Original languageEnglish
Pages (from-to)16
Number of pages6
JournalStudia mathematica
Volume179
Issue number1
DOIs
Publication statusPublished - 2007

Keywords

  • Hardy space
  • uniformly discrete sequence
  • uniformly separated sequence
  • Bergman space
  • INTERPOLATION SEQUENCES
  • ANALYTIC FUNCTIONS
  • CARLESON

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