A probabilistic approach to hp(Rd)

Srinivasa 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

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Brownian movement
Probabilistic Approach
Mathematical operators
Interpolation
Bounded Mean Oscillation
Integrability
Brownian motion
Interpolate
Operator
Theorem
Relationships

Keywords

  • Harmonic functions
  • Interpolation
  • Martingale. Wiener measure

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A probabilistic approach to hp(Rd). / Varadhan, Srinivasa; Stroock, D.; Words, Key.

In: Transactions of the American Mathematical Society, Vol. 192, 1974, p. 245-260.

Research output: Contribution to journalArticle

Varadhan, Srinivasa ; Stroock, D. ; Words, Key. / A probabilistic approach to hp(Rd). In: Transactions of the American Mathematical Society. 1974 ; Vol. 192. pp. 245-260.
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