Subspaces of

Author:
Michael Frazier

Journal:
Trans. Amer. Math. Soc. **290** (1985), 101-125

MSC:
Primary 42B20; Secondary 42B30, 46E99, 47G05

MathSciNet review:
787957

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Abstract: We consider subspaces of generated by one singular integral transform. We show that the averages along -lines of the th Riesz transform of or satisfy a certain strong regularity property. One consquence of this result is that such functions satisfy a uniform doubling condition on a.e. -line. We give an example to show, however, that the restrictions to -lines of the Riesz transform of do not necessarily have uniformly bounded norm. Also, for a Calderón-Zygmund singular integral operator with real and odd kernel, we show that , where and are the spaces of or functions of compact support, respectively, and the closure is taken in norm.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1985-0787957-0

Keywords:
,
singular integral operator

Article copyright:
© Copyright 1985
American Mathematical Society