Characterizations of Hankel multipliers |
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Authors: | Gustavo Garrigós Andreas Seeger |
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Institution: | (1) Dep. Matemáticas C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain;(2) Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA |
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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.
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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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 42B15 |
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