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<p>The purpose of this paper is to study noncommutative Bochner–Riesz means associated with Fourier–Bessel expansions. More precisely, we establish the noncommutative maximal inequalities for this operator and then prove the corresponding pointwise convergence theorems. Moreover, by using the noncommutative Hilber-valued Calderón–Zygmund theory, we also investigate the mapping properties for noncommutative Littlewood–Paley–Stein <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>g</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>-functions related to the Poisson semigroup of Fourier–Bessel expansions for each <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Noncommutative Bochner–Riesz means associated with Fourier–Bessel expansions

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Wei Li,
  • Lian Wu,
  • Yahui Zuo

摘要

The purpose of this paper is to study noncommutative Bochner–Riesz means associated with Fourier–Bessel expansions. More precisely, we establish the noncommutative maximal inequalities for this operator and then prove the corresponding pointwise convergence theorems. Moreover, by using the noncommutative Hilber-valued Calderón–Zygmund theory, we also investigate the mapping properties for noncommutative Littlewood–Paley–Stein \(g_k\) g k -functions related to the Poisson semigroup of Fourier–Bessel expansions for each \(k\ge 1\) k ≥ 1 .