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<p>In the present paper, we introduce and study the concept of a Weinstein wavelet multiplier and establish its trace formula as a bounded linear operator in the trace class from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( L^2_\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>L</mi> <mi>ω</mi> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> to itself, expressed in terms of its symbol and two admissible wavelets. Additionally, we provide results concerning the boundedness and compactness of Weinstein wavelet multipliers on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( L^p_\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>L</mi> <mi>ω</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( 1 \le p \le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Boundedness and compactness analysis of the weinstein wavelet multipliers

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Ahmed Saoudi

摘要

In the present paper, we introduce and study the concept of a Weinstein wavelet multiplier and establish its trace formula as a bounded linear operator in the trace class from \( L^2_\omega \) L ω 2 to itself, expressed in terms of its symbol and two admissible wavelets. Additionally, we provide results concerning the boundedness and compactness of Weinstein wavelet multipliers on \( L^p_\omega \) L ω p for \( 1 \le p \le \infty \) 1 ≤ p ≤ ∞ .