Modified logarithmic potential theory and applications

A function Class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions

In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite . We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions.

Hardy算子在 $L^{1}(0,\infty)$ 和 $\ell^1$ 上的精确对数条件

A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$

本文研究了Hardy算子在 $L^{1}(0,\infty)$ 和 $\ell^1$ 上的有界性问题，引入修正后的Hardy算子并确定其可映射到可积函数空间的最大子空间，得出一个精确的对数可积性条件。

修正贝塞尔函数乘积及其对数导数的尖锐双侧界

Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative

本文为修正贝塞尔函数乘积及其对数导数之和建立了带最优常数的尖锐双侧不等式，证明基于辅助函数的二阶微分不等式与强极大值原理，并应用于乘积单调性和比值改进。

对数双层位势到Ahlfors-正则边界的连续延拓

The continuous extension of the logarithmic double layer potential to the Ahlfors-regular boundary

本文研究Cauchy型积分实部（即双层对数位势）的边界行为，给出了其到Ahlfors-正则边界连续延拓的充要条件。

Functional inequalities involving modified Struve functions

In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional inequalities (like Turán type inequalities) as well as lower and upper bounds for modified Struve function of the second kind and its logarithmic derivative.

The singular values of the logarithmic potential transform on bound states spaces of Landau Hamiltonian

The singular values of the logarithmic potential transform on the generalized Bergmann space is calculated explicitly, too behavior in infinity