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<p>In this paper, we consider a type of square functions in difference form, which is a modified one of sharp-edged square functions introduced by Wilson. By adding Lipschitz conditions on the constituent kernels of the square functions, we show that they are bounded on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^p(\mathbb {R}^d)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(p\in (1,\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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\(L^p\) Boundedness of Some Square Functions in Difference Form

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Junqiang Zhang,
  • Yuting Zhou

摘要

In this paper, we consider a type of square functions in difference form, which is a modified one of sharp-edged square functions introduced by Wilson. By adding Lipschitz conditions on the constituent kernels of the square functions, we show that they are bounded on \(L^p(\mathbb {R}^d)\) L p ( R d ) for all \(p\in (1,\infty )\) p ∈ ( 1 , ∞ ) .