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
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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