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<p>We prove that the best constant in the weak type (1, 1) inequality for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\rho\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation>-variation operator associated with the Poisson semigroup grows at most like <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(O(n^{3/2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow> <mn>3</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Moreover, we provide a limit result for the weak type (1, 1) bound.</p>

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The weak type (1, 1) bounds for the \(\rho\)-variation operator associated with the Poisson semigroup

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • J. Wang,
  • H. Li,
  • H. Liu

摘要

We prove that the best constant in the weak type (1, 1) inequality for the \(\rho\) ρ -variation operator associated with the Poisson semigroup grows at most like \(O(n^{3/2})\) O ( n 3 / 2 ) . Moreover, we provide a limit result for the weak type (1, 1) bound.