Pencho Petrushev, Yuan Xu
Published 2007-05-02Version 1
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.
Littlewood-Paley decompositions and Besov spaces related to symmetric cones
On the $L^2$ boundedness of pseudo-multipliers for Hermite expansions
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
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