Scholarlink

<p>We prove that the lacunary spherical maximal operator, defined on the <i>n</i>-dimensional real hyperbolic space, is bounded on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p(\mathbb {H}^n)\)</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">H</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(1&lt;p\le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Lacunary spherical maximal operators on hyperbolic spaces

  • 期刊论文

  • 发表日期：

    2026年5月29日

查看全文
  • Yunxiang Wang,
  • Hong-Wei Zhang

摘要

We prove that the lacunary spherical maximal operator, defined on the n-dimensional real hyperbolic space, is bounded on \(L^p(\mathbb {H}^n)\) L p ( H n ) for all \(n\ge 2\) n ≥ 2 and \(1<p\le \infty \) 1 < p ≤ ∞ . In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space.