Multilinear Fourier multipliers with minimal Sobolev regularity(2)

DOI DOI Web Site 参考文献20件

書誌事項

タイトル別名
  • Multilinear Fourier multipliers with minimal Sobolev regularity, II

この論文をさがす

説明

<p>We provide characterizations for boundedness of multilinear Fourier multiplier operators on Hardy or Lebesgue spaces with symbols locally in Sobolev spaces. Let Hq(ℝn) denote the Hardy space when 0 < q ≤ 1 and the Lebesgue space Lq(ℝn) when 1 < q ≤ ∞. We find optimal conditions on m-linear Fourier multiplier operators to be bounded from Hp1 × … × Hpm to Lp when 1/p = 1/p1 + … + 1/pm in terms of local L2-Sobolev space estimates for the symbol of the operator. Our conditions provide multilinear analogues of the linear results of Calderón and Torchinsky [1] and of the bilinear results of Miyachi and Tomita [17]. The extension to general m is significantly more complicated both technically and combinatorially; the optimal Sobolev space smoothness required of the symbol depends on the Hardy–Lebesgue exponents and is constant on various convex simplices formed by configurations of m2m−1 + 1 points in [0,∞)m.</p>

収録刊行物

参考文献 (20)*注記

もっと見る

関連プロジェクト

もっと見る

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ