Geodesic
Spectral decompositions and harmonic analysis on UMD spaces
Studia Mathematica, Tome 112 (1994) no. 1, pp. 13-49

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for $L_X^p$ to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.
DOI : 10.4064/sm-112-1-13-49

Earl Berkson 1 ; T. A.  1

1 
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Earl Berkson; T. A. . Spectral decompositions and harmonic analysis on UMD spaces. Studia Mathematica, Tome 112 (1994) no. 1, pp. 13-49. doi: 10.4064/sm-112-1-13-49

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