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A Cesaro Average of Hardy-Littlewood numbers
Goldbach-type theorems Hardy-Littlewood numbers Laplace transforms Cesaro averages
2012/6/14
Let $\Lambda$ be the von Mangoldt function and (r_{\textit{HL}}(n) = \sum_{m_1 + m_2^2 = n} \Lambda(m_1),) be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently large in...
Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data
semigroup Riemannian manifolds singular data
2010/11/12
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initial condition. We sho...
A Reverse Hardy-Hilbert-Type Integral Inequality
Hardy-Hilbert-type integral inequality weight function $beta$ function Holder's inequality
2010/1/25
By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have be...
本文给出了加权Hardy--Littlewood平均算子 $U_{\psi}$在Herz空间 $\dot{K}^{\alpha,p}_q({\rm R}^n)$中有界的充分必要条件并估计了相应的算子范数.