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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Weak type estimates for Bochner-Riesz spherical summation multipliers
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by Sagun Chanillo and Benjamin Muckenhoupt
Trans. Amer. Math. Soc. 294 (1986), 693-703
DOI: https://doi.org/10.1090/S0002-9947-1986-0825730-6

Abstract:

We consider the Bochner-Riesz multiplier \[ \widehat {{T_\delta }f}(\xi ) = {(1 - {\left | \xi \right |^2})^\delta } + \hat f(\xi ),\qquad \delta > 0,\] where $\widehat {}$ denotes the Fourier transform. It is shown that the multiplier operator ${T_\delta }$ is weak type $({p_0}, {p_0})$ acting on ${L^{p0}}({{\mathbf {R}}^n})$ radial functions, where ${p_0}$ is the critical value $2n/(n + 1 + 2\delta )$.
References
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Bibliographic Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 693-703
  • MSC: Primary 42B20; Secondary 44A15
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825730-6
  • MathSciNet review: 825730