Weak restricted and very restricted operators on

Author:
J. Marshall Ash

Journal:
Trans. Amer. Math. Soc. **281** (1984), 675-689

MSC:
Primary 42A45; Secondary 42A50, 47B38

MathSciNet review:
722768

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Abstract: A battlement is a real function with values in that looks like a castle battlement. A commuting with translation linear operator mapping step functions on into the set of all measurable functions on and satisfying for all battlements is bounded on . This remains true if the underlying space is the circle but is demonstrably false if the underlying space is the integers. Michael Cowling's theorem that linear commuting with translation operators are bounded on if they are weak restricted is reproved and an application of this result to sums of exponentials is given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0722768-2

Keywords:
Operator,
weak restricted type ,
commuting with translation,
convolution operator,
multiplier

Article copyright:
© Copyright 1984
American Mathematical Society