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<p>We investigate the essential norms of weighted composition operators and the differences of such operators acting between weighted Bergman spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {A}_{\omega }^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">A</mi> <mrow> <mi>ω</mi> </mrow> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation>, with a focus on almost standard radial weights. Motivated by the complexity of existing approaches that depend extensively on Carleson measures, we derive easily computable criteria for the compactness of weighted composition operators. Consequently, these criteria yield explicit estimates for the essential norms of such operators, and of their differences, including both lower and upper bounds, improving the best known bounds.</p>

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A new characterization for the essential norm of weighted composition operators and their differences on weighted Bergman spaces

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Kobra Esmaeili

摘要

We investigate the essential norms of weighted composition operators and the differences of such operators acting between weighted Bergman spaces \(\mathcal {A}_{\omega }^{p}\) A ω p , with a focus on almost standard radial weights. Motivated by the complexity of existing approaches that depend extensively on Carleson measures, we derive easily computable criteria for the compactness of weighted composition operators. Consequently, these criteria yield explicit estimates for the essential norms of such operators, and of their differences, including both lower and upper bounds, improving the best known bounds.