Abstract
In this work we present several theorems which imply the weak type 1 with respect to the Gaussian measure for the so-called local part of certain operators associated with the Ornstein-Uhlenbeck semigroup. Particular cases of these operators are the Riesz transforms of any order and the Littlewood-Paley square function. Also, we study general results based on the “size” of the operator which ensure the strong type 1 <p < ∞of both the local and global parts.
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Communicated by Guido Weiss
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Pérez, S. The local part and the strong type for operators related to the Gaussian measure. J Geom Anal 11, 491–507 (2001). https://doi.org/10.1007/BF02922016
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DOI: https://doi.org/10.1007/BF02922016