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arXiv · 1407.2141

Multilinear Fourier multipliers on variable Lebesgue spaces

Jineng Ren·Wenchang Sun
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Abstract

In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem of multipliers on variable exponent Lebesgue spaces. Moreover, we present a Mihlin-Hörmander type theorem for multilinear Fourier multipliers on weighted variable Lebesgue spaces and give some applications.

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Jineng Ren, Wenchang Sun. 2014-07-08. Multilinear Fourier multipliers on variable Lebesgue spaces. https://arxiv.org/abs/1407.2141

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