<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$H^n(\mathbb {R})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> denote the real hyperbolic space realized as the symmetric space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${{\,\textrm{Spin}\,}}_0(1,n)/{{\,\textrm{Spin}\,}}(n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mspace width="0.166667em" /> <mtext>Spin</mtext> <mspace width="0.166667em" /> </mrow> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <mrow> <mspace width="0.166667em" /> <mtext>Spin</mtext> <mspace width="0.166667em" /> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we provide a characterization for the image of the Poisson transform for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$L^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-sections of the spinor bundle over the boundary <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\partial H^n({\mathbb {R}})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <msup> <mi>H</mi> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. As a consequence, we obtain an <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$L^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> uniform estimate for the generalized spectral projections associated to the spinor bundle over <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$H^n({\mathbb {R}})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, thereby extending Strichartz’s conjecture from the scalar case to the spinor setting.</p>

Strichartz’s conjecture for the spinor bundle over the real hyperbolic space

期刊论文
发表日期：

2026年2月12日

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Abdelhamid Boussejra,
Khalid Koufany

摘要

Let $H^n(\mathbb {R})$ $H^{n} (R)$ denote the real hyperbolic space realized as the symmetric space ${{\,\textrm{Spin}\,}}_0(1,n)/{{\,\textrm{Spin}\,}}(n)$ ${Spin}_{0} (1, n) / Spin (n)$ . In this paper, we provide a characterization for the image of the Poisson transform for $L^2$ $L^{2}$ -sections of the spinor bundle over the boundary $\partial H^n({\mathbb {R}})$ $\partial H^{n} (R)$ . As a consequence, we obtain an $L^2$ $L^{2}$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n({\mathbb {R}})$ $H^{n} (R)$ , thereby extending Strichartz’s conjecture from the scalar case to the spinor setting.