The bilinear Bochner-Riesz problem
نویسندگان
چکیده
Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for larger values of δ. Our study is broad enough to encompass general bilinear multipliers m(ξ, η) radial in ξ and η with minimal smoothness, measured in Sobolev space norms. The results obtained are based on a variety of techniques, that include Fourier series expansions, orthogonality, and bilinear restriction and extension theorems.
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