Scholarlink

<p>We study matrix-weighted bounds for a class of sublinear non-kernel operators considered by F.&#xa0;Bernicot, D.&#xa0;Frey, and S.&#xa0;Petermichl, whose work did not include vector-valued functions. The main feature of our approach is the use of sparse bilinear convex body domination, adapted from a recent general principle due to T.&#xa0;Hytönen, which does not apply to the sublinear case. This sparse domination framework allows us to adapt and extend techniques from F.&#xa0;Nazarov, S.&#xa0;Petermichl, S.&#xa0;Treil, and A.&#xa0;Volberg to the matrix-weighted setting. This approach leads to sharper matrix-weighted norm estimates than the ones previously known. Our weight assumptions are formulated in terms of two-exponent matrix Muckenhoupt conditions, which reveal a surprisingly rich structure absent in the scalar setting. Moreover, we establish a limited range extrapolation theorem for matrix weights, which is more general than the one in the earlier work by P.&#xa0;Auscher and J.&#xa0;M.&#xa0;Martell, as well as M.&#xa0;Bownik and D.&#xa0;Cruz-Uribe. This highlights the versatility and potential of our approach for broader applications in weighted harmonic analysis.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Matrix-weighted estimates beyond Calderón–Zygmund theory

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月18日

查看全文
  • Spyridon Kakaroumpas,
  • Thu Hien Nguyen,
  • Dimitris Vardakis

摘要

We study matrix-weighted bounds for a class of sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl, whose work did not include vector-valued functions. The main feature of our approach is the use of sparse bilinear convex body domination, adapted from a recent general principle due to T. Hytönen, which does not apply to the sublinear case. This sparse domination framework allows us to adapt and extend techniques from F. Nazarov, S. Petermichl, S. Treil, and A. Volberg to the matrix-weighted setting. This approach leads to sharper matrix-weighted norm estimates than the ones previously known. Our weight assumptions are formulated in terms of two-exponent matrix Muckenhoupt conditions, which reveal a surprisingly rich structure absent in the scalar setting. Moreover, we establish a limited range extrapolation theorem for matrix weights, which is more general than the one in the earlier work by P. Auscher and J. M. Martell, as well as M. Bownik and D. Cruz-Uribe. This highlights the versatility and potential of our approach for broader applications in weighted harmonic analysis.