Weighted norm inequalities for Bochner-Riesz spherical summation multipliers

Andersen, Kenneth F.

doi:10.1090/S0002-9939-1988-0938663-9

Weighted norm inequalities for Bochner-Riesz spherical summation multipliers
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by Kenneth F. Andersen

Proc. Amer. Math. Soc. 103 (1988), 165-171

DOI: https://doi.org/10.1090/S0002-9939-1988-0938663-9

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Abstract:

Sufficient conditions to be satisfied by nonnegative weight functions $\omega \left ( {\left | x \right |} \right )$ are given in order that the Bochner-Riesz spherical summation multiplier operators restricted to radial functions of ${R^n}$ be bounded on ${L^p}\left ( {{R^n};\omega \left ( {\left | x \right |} \right )dx} \right )$. For a certain class of weights these conditions are also necessary.

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