A probabilistic approach to hp(Rd)

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

doi:10.1090/S0002-9947-1974-0365696-0

A probabilistic approach to h^p(R^d)

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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The relationship between H^p(R^d), 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(R^d) to L¹(R^d).

Original language	English (US)
Pages (from-to)	245-260
Number of pages	16
Journal	Transactions of the American Mathematical Society
Volume	192
DOIs	https://doi.org/10.1090/S0002-9947-1974-0365696-0
State	Published - 1974

Keywords

Harmonic functions
Interpolation
Martingale. Wiener measure

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-1974-0365696-0

Cite this

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title = "A probabilistic approach to hp(Rd)",

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).",

keywords = "Harmonic functions, Interpolation, Martingale. Wiener measure",

author = "Varadhan, {S. R.S.} and D. Stroock and Key Words",

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AU - Varadhan, S. R.S.

AU - Stroock, D.

AU - Words, Key

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AB - 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).

KW - Harmonic functions

KW - Interpolation

KW - Martingale. Wiener measure

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JO - Transactions of the American Mathematical Society

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