Scholarlink

<p>The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a “suitable class” of test functions, we show that, under quite general assumptions (essentially minimal ones to make sense of the formula), the representation is actually valid for all pairs (<i>f,g</i>) ∈ <i>L</i><sup><i>p</i></sup>(ℝ<sup><i>d</i></sup>) × <i>L</i><sup><i>p</i>′</sup>(ℝ<sup><i>d</i></sup>), not just test functions.</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

On the Sense of Convergence in the Dyadic Representation Theorem

  • 期刊论文

  • 发表日期：

    2025年1月15日

查看全文
  • Tuomas Hytönen

摘要

The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a “suitable class” of test functions, we show that, under quite general assumptions (essentially minimal ones to make sense of the formula), the representation is actually valid for all pairs (f,g) ∈ Lp(ℝd) × Lp′(ℝd), not just test functions.