Sufficiency conditions for multipliers with general weights

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

Journal:
Trans. Amer. Math. Soc. **300** (1987), 463-502

MSC:
Primary 42A45; Secondary 42B15

DOI:
https://doi.org/10.1090/S0002-9947-1987-0876462-0

MathSciNet review:
876462

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Abstract: Weighted norm inequalities in are proved for multiplier operators with the multiplier function satisfying Hörmander type conditions. 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 a larger class of weight functions than usually considered; weight functions used here are of the form where ) is a polynomial of arbitrarily high degree and is in . For weight functions in , the results hold for all Schwartz functions. The periodic case is also considered.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0876462-0

Article copyright:
© Copyright 1987
American Mathematical Society