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Littlewood-Paley theory on Gaussian spaces

Published online by Cambridge University Press:  22 January 2016

Jürgen Potthoff
Jürgen Potthoff*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya 464, Japan, and Department of Mathematics, MA7-1, Technical University Berlin, Strasse d. 17. Juni 135, D-1000, Berlin, 12
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In this article we prove a number of inequalities of Littlewood-Paley-Stein (LPS) type for functions on general Gaussian spaces (s. below).

In finite dimensional Euclidean spaces (with Lebesgue measure) the power of such inequalities has been demonstrated in Stein’s book [12]. In his second book [13], Stein treats other spaces too: also the situation of a general measure space (X, μ). However the latter case is too general to allow for a rich class of inequalities (cf. Theorem 10 in [13]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 47 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

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