论文标题
$ l^p-l^q $与Anharmonic振荡器相关的傅立叶乘数的有界性
$L^p-L^q$ boundedness of Fourier multipliers associated with the anharmonic Oscillator
论文作者
论文摘要
在本文中，我们研究了傅立叶乘数的$ l^p $ - $ l^q $有界的环境，在该环境中，基础傅立叶分析被引入了关于非谐波振荡器$ a $ a $的特征函数。使用此分析产生的全局符号的概念，我们扩展了Hausdorff-Young-paley不平等的版本，该版本可以保证这些操作员的$ l^p $ - $ l^q $界限的范围为$ 1 <p \ leq 2 \ leq 2 \ leq q <\ q <\ f iftty $。获取的光谱乘数的界限结果，作为特定情况嵌入定理的特定情况和与Anharmonic振荡器相关的热核的$ l^p $ - $ l^q $规范的特定情况。此外，我们考虑了在调制空间上的Anharmonic振荡器的功能$ F（a）$，并证明Linsk \ u II的跟踪公式即使$ f（a）$只是核操作员，即使$ f（a）$也是如此。
In this paper we study the $L^p$-$L^q$ boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator $A$. Using the notion of a global symbol that arises from this analysis, we extend a version of the Hausdorff-Young-Paley inequality that guarantees the $L^p$-$L^q$ boundedness of these operators for the range $1<p \leq 2 \leq q <\infty$. The boundedness results for spectral multipliers acquired, yield as particular cases Sobolev embedding theorems and time asymptotics for the $L^p$-$L^q$ norms of the heat kernel associated with the anharmonic oscillator. Additionally, we consider functions $f(A)$ of the anharmonic oscillator on modulation spaces and prove that Linsk\u ii's trace formula holds true even when $f(A)$ is simply a nuclear operator.
