A probabilistic approach to hp(Rd)

S. R.S. Varadhan, D. Stroock, Key Words

Research output: Contribution to journalArticle

Abstract

The relationship between Hp(Rd), 1 ≤ p < ¥, and the integrability of certain functionals of Brownian motion is established using the connection between probabilistic and analytic notions of functions with bounded mean oscillation. An application of this relationship is given in the derivation of an interpolation theorem for operators taking H1(Rd) to L1(Rd).

Original languageEnglish (US)
Pages (from-to)245-260
Number of pages16
JournalTransactions of the American Mathematical Society
Volume192
DOIs
StatePublished - 1974

Keywords

  • Harmonic functions
  • Interpolation
  • Martingale. Wiener measure

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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