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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Hörmander type criterion for quasiradial Fourier multipliers
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by Henry Dappa and Hajo Luers PDF
Proc. Amer. Math. Soc. 95 (1985), 419-424 Request permission

Abstract:

We state practicable sufficient conditions on quasi-radial functions $m \circ \rho (\xi ) = m(\rho (\xi ))$ to be Fourier multipliers in ${L^p}({{\mathbf {R}}^n})$. Here $m$ is a bounded function and $\rho$ is a homogeneous distance function. The conditions on $m$ are given in terms of localized Bessel potentials and those on $\rho$ reflect and generalize basic properties of the norm in ${{\mathbf {R}}^n}$. The results are related to those of Madych [7] and Fabes and Rivière [3] and improve their results (specialized to quasi-radial multipliers). The proof utilizes Madych’s approach [7] and interpolation properties of localized Bessel potential spaces [2].
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 419-424
  • MSC: Primary 42B15; Secondary 46E35
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0806080-5
  • MathSciNet review: 806080