Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

• Miyachi, Akihiko ^[2] ; Shida, Naoto ^[1] ; Tomita, Naohito ^[1]
  1. [1] Osaka University

     Osaka University

     Kita Ku, Japón

     
  2. [2] Department of Mathematics, Tokyo Woman’s Christian University, Zempukuji, Suginami-ku, Tokyo, 167-8585, Japan
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 307-332
• Idioma: inglés
• DOI: 10.1007/s13348-020-00289-z
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• Resumen

  • In this paper, the L2×L∞→L2 and L2×L2→L1 estimates of bilinear Fourier multiplier operators are discussed under weak smoothness conditions on multipliers. As an application, we prove the L2×BMO→L2 and L2×L2→H1 boundedness of bilinear operators with multipliers of limited smoothness satisfying vanishing conditions.