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Sergei
  • Member for 10 years, 8 months
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  • Voronezh, Russia
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generalized mean inequality extension
Above are norm inequalities. Devide by n with proper powers and they will reduce to means inequalities with best constants. Not so?
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generalized mean inequality extension
$||x||_p \le ||x||_r \le n^{1/r-1/p} ||x||_p$,
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generalized mean inequality extension
In Wiki we find exact inequalities: for $p>r>0$ it follows
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generalized mean inequality extension
In fact power means are norms on finite dimensional spaces. All such norms are equivalent, so the inequalities you asked for exist and constants in them are embedding space theorems constants.
awarded
 Yearling
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Constructing a quasiconvex function
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Motivating the Bessel translation operator
It is also easy to generalize in this particular PDE form, just change a pair of differential operators $(B_\alpha,D^2)$ to another pair.
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Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?
Is not it possible to find this sum explicitly as in case of the Gauss sum it looks like?
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Motivating the Bessel translation operator
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Is there any simpler form of this function
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A "quadratic" triangular inequality
awarded
 Peer Pressure
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Coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$
2. May you give a reference please where such theta-like functions are studied.
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Coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$
1. You consider convergent or formal series?
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Cauchy-Schwarz inequality for bilinear forms valued in an abstract vector space
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An upper bound for the difference between arithmetic and harmonic mean
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convolution integral involving modified Bessel functions of the first kind
So the integral in your question is $\int_0^z$?
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convolution integral involving modified Bessel functions of the first kind
$z-x$ can be negative, its powers are complex numbers. For the integral it seems the only reasonable way is to use series for the second modified Bessel function and try after integration to sum up somehow.
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convolution integral involving modified Bessel functions of the first kind
How to define $(z-x)^{1/2\mu}$ in this integral?
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Transforming a recurrence to the product of two other recurrences
$a_2$ is even. So all next $a_n$ for $n\ge 2$ are even too and so composite.
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