Multilinear Fourier Multipliers with Minimal Sobolev Regularity
نویسنده
چکیده
Letm be a positive integer. In this talk, we will introduce optimal conditions,expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operatorsto be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces.Our results are sharp and cover the bilinear case (m = 2) obtained by Miyachiand Tomita [1]. References[1] Miyachi A., and Tomita N., Minimal smoothness conditions for bilinearFourier multipliers. Rev. Mat. Iberoamer. 29 (2013), no. 2, 495–530.
منابع مشابه
Multilinear Fourier Multipliers with Minimal Sobolev Regularity, I
We find optimal conditions on m-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces Hj , 0 < pj ≤ 1, to Lebesgue spaces Lp. The conditions we obtain are necessary and sufficient for boundedness and are expressed in terms of L2-based Sobolev spaces. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky [1] and in the bilin...
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