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<p>We propose a survey on composition operators acting in Sobolev spaces including their continuity and the Faà di Bruno’s formula, together with similar properties for composition operators in homogeneous Adams-Frazier spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\dot{W}^m_p\cap \dot{W}^1_{mp}({\mathbb {R}}^n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mover accent="true"> <mi>W</mi> <mo>˙</mo> </mover> <mi>p</mi> <mi>m</mi> </msubsup> <mo>∩</mo> <msubsup> <mover accent="true"> <mi>W</mi> <mo>˙</mo> </mover> <mrow> <mi mathvariant="italic">mp</mi> </mrow> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Composition in Sobolev Spaces : A Unified Approach

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Gérard Bourdaud

摘要

We propose a survey on composition operators acting in Sobolev spaces including their continuity and the Faà di Bruno’s formula, together with similar properties for composition operators in homogeneous Adams-Frazier spaces \(\dot{W}^m_p\cap \dot{W}^1_{mp}({\mathbb {R}}^n)\) W ˙ p m ∩ W ˙ mp 1 ( R n ) .