In this paper, we consider weighted norm inequalities for multilinear Fourier multipliers. Our result can be understood as a multilinear version of the result by Kurtz and Wheeden.

In this paper, weighted norm inequalities for multilinear Fourier multipliers with Besov regularity are discussed. As a result, we obtain a limiting case of Hörmander type multiplier theorem for multilinear operators.

The problem whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.2010 Mathematics Subject Classification. 42B15, 42B20, 42B25.

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