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On an inequality for the Riemann zeta-function in the critical strip
Riemann zeta-function size of the Riemann zeta-function new inequalities critical strip
2012/6/30
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we est...
An Optimal Inequality For The Tangent Function
inequality tangent function power series expansion
2012/5/24
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents invol...
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfet...
The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group
Yamabe equation quaternionic contact structures
2010/12/7
We determine the best (optimal) constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group and the non-negative functions for which equality holds.
A weak Harnack inequality for fractional evolution equations with discontinuous coefficients
weak Harnack inequality Moser iterations fractional derivativ weak solutions
2010/12/13
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a unifo...
In this note we prove a generalized version of an inequality which was first introduced by A. Q. Ngo, et al. and later generalized and proved by W. J. Liu, et al. in the paper: "On an open problem con...