Spectral decompositions and harmonic analysis on UMD spaces

Berkson, Earl; Gillespie, T.

Studia Mathematica, Tome 108 (1994), p. 13-49 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1994-01-01

Zbl 0823.42004

EUDML-ID : urn:eudml:doc:216134

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     author = {Earl Berkson and T. Gillespie},
     title = {Spectral decompositions and harmonic analysis on UMD spaces},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {13-49},
     zbl = {0823.42004},
     language = {en},
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Berkson, Earl; Gillespie, T. Spectral decompositions and harmonic analysis on UMD spaces. Studia Mathematica, Tome 108 (1994) pp. 13-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i1p13bwm/

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