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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weak type estimates for Bochner-Riesz spherical summation multipliers
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by Sagun Chanillo and Benjamin Muckenhoupt PDF
Trans. Amer. Math. Soc. 294 (1986), 693-703 Request permission

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 $2n/(n + 1 + 2\delta )$.
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Additional 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