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Hermite Conjugate Functions and Rearrangement Invariant Spaces

Published online by Cambridge University Press:  20 November 2018

Kenneth F. Andersen
Kenneth F. Andersen*
Affiliation:
University of Alberta, Edmonton, Alberta.
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The Hermite conjugate Poisson integral of a given f ∊ L1(μ), dμ(y)= exp(—y2) dy, was defined by Muckenhoupt [5, p. 247] as

where

If the Hermite conjugate function operator T is defined by (Tf) a.e., then one of the main results of [5] is that T is of weak-type (1, 1) and strongtype (p,p) for all p>l.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 377 - 380
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Andersen, K. F., Discrete Hilbert transformations on rearrangement invariant sequence spaces, Thesis, University of Toronto, 1970.Google Scholar
2. Boyd, D. W., The Hilbert transform on rearrangement invariant spaces, Canad. J. Math. 19 (1967), 599–616.Google Scholar
3. Boyd, D. W., Indices of function spaces and their relationship to interpolation, Canad. J. Math. 21 (1969), 1245–1254.Google Scholar
4. Kerman, R. A., Conjugate functions and rearrangement invariant spaces, Thesis, University of Toronto, 1969.Google Scholar
5. Muckenhoupt, B., Hermite conjugate expansions, Trans. Amer. Math. Soc. 139 (1969), 243–260.Google Scholar
6. Ryan, R., Conjugate functions in Orlicz spaces, Pacific J. Math. 13 (1963), 1371–1377.Google Scholar