Abstract
We give characterizations of radial Fourier multipliers as acting on radial L p functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L p − L q bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include results on interpolation of multiplier spaces.
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G. Garrigós partially supported by grant “MTM2007-60952” and Programa Ramón y Cajal, MCyT (Spain). A. Seeger partially supported by NSF grant DMS 0652890.
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Garrigós, G., Seeger, A. Characterizations of Hankel multipliers. Math. Ann. 342, 31–68 (2008). https://doi.org/10.1007/s00208-008-0221-8
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DOI: https://doi.org/10.1007/s00208-008-0221-8