Sufficiency conditions for -multipliers with power weights

Authors:
Benjamin Muckenhoupt, Richard L. Wheeden and Wo-Sang Young

Journal:
Trans. Amer. Math. Soc. **300** (1987), 433-461

MSC:
Primary 42A45; Secondary 42B15

DOI:
https://doi.org/10.1090/S0002-9947-1987-0876461-9

MathSciNet review:
876461

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Abstract: Weighted norm inequalities in are proved for multiplier operators with the multiplier function of Hörmander type. The operators are initially defined on the space of Schwartz functions whose Fourier transforms have compact support not including 0. This restriction on the domain of definition makes it possible to use weight functions of the form for larger than usually considered. For these weight functions, if is not an integer, a strict inequality on is shown to be sufficient for a norm inequality to hold. A sequel to this paper shows that the weak version of this inequality is necessary.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0876461-9

Article copyright:
© Copyright 1987
American Mathematical Society