论文标题
关于一般双重措施及其应用的交集的结构定理
A Structure Theorem on Intersections of General Doubling Measures and Its Applications
论文作者
论文摘要
我们通过研究谐波分析中的Hasse原理失败的类似物来将两个主题在二元分析和数理论中结合在一起。明确地，我们在实际线路上构建了一个明确的措施家族，即$ p $ - adiC和$ q $ - ad的二倍，但对于任何独特的素数$ p $和$ q $，但没有翻倍，我们将这些结果应用于反向Hölder和Muckenhoupt $ a_p $ a_p $ a_p $ agy a_p $类别的类似陈述。证明涉及几种几何和数理论特性之间的微妙相互作用。
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are $p$-adic and $q$-adic doubling for any distinct primes $p$ and $q$, yet not doubling, and we apply these results to show analogous statements about the reverse Hölder and Muckenhoupt $A_p$ classes of weights. The proofs involve a delicate interplay among several geometric and number theoretic properties.
