Multiplier Transformations of Weak Type

Multiplier Transformations of Weak Type

Let$1 < p < 2$. On several of the classical groups arising in Fourier analysis, including the n-torus and Euclidean n-space, we show that there exists a multiplier which is of weak type (p, p), but which is not bounded on Lp.

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Veröffentlicht in:Annals of mathematics 1975-01, Vol.101 (1), p.34-44
1. Verfasser: Zafran, Misha
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Fourier analysis
Fourier transformations
Integers
Interpolation
Linear transformations
Mathematical inequalities
Mathematical integrals
Mathematical theorems
Series convergence
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Beschreibung
Zusammenfassung:Let$1 < p < 2$. On several of the classical groups arising in Fourier analysis, including the n-torus and Euclidean n-space, we show that there exists a multiplier which is of weak type (p, p), but which is not bounded on Lp.
ISSN:0003-486X
DOI:10.2307/1970985