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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A probabilistic approach to $ H\sp{p}(R\sp{d})$


Authors: D. Stroock and S. R. S. Varadhan
Journal: Trans. Amer. Math. Soc. 192 (1974), 245-260
MSC: Primary 60G45; Secondary 42A36
DOI: https://doi.org/10.1090/S0002-9947-1974-0365696-0
MathSciNet review: 0365696
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Abstract: The relationship between $ {H^p}({R^d}),1 \leq p < \infty $, 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 $ {H^1}({R^d})$ to $ {L^1}({R^d})$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0365696-0
Keywords: Martingale, Wiener measure, harmonic functions, interpolation
Article copyright: © Copyright 1974 American Mathematical Society