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On the volume of unit balls of finite-dimensional Lorentz spaces
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-03-14 , DOI: 10.1016/j.jat.2020.105407 Anna Doležalová , Jan Vybíral
中文翻译:
关于有限维洛伦兹空间的单位球的体积
更新日期:2020-03-14
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-03-14 , DOI: 10.1016/j.jat.2020.105407 Anna Doležalová , Jan Vybíral
We study the volume of unit balls of finite-dimensional Lorentz sequence spaces We give an iterative formula for for the weak Lebesgue spaces with and explicit formulas for and We derive asymptotic results for the th root of and show that for all and We study further the ratio between the volume of unit balls of weak Lebesgue spaces and the volume of unit balls of classical Lebesgue spaces. We conclude with an application of the volume estimates and characterize the decay of the entropy numbers of the embedding of the weak Lebesgue space into
中文翻译:
关于有限维洛伦兹空间的单位球的体积
我们研究单位球的体积 维洛伦兹序列空间的集合 我们给出一个迭代公式 对于弱的Lebesgue空间 和明确的公式 和 我们得出了渐近结果 的根 并表明 对所有人 和 我们进一步研究弱Lebesgue空间的单位球的体积与经典Lebesgue空间的单位球的体积之比。我们以体积估计值的应用结束,并刻画了弱Lebesgue空间嵌入的熵数的衰减 进入