Abstract:
We will talk on three results:
1. The operator $D\Delta^{-1}div$ in $L_2(R^n)$ with power weight – the exact value of its norm.
2. The operator $D^s\Delta^{-(s+t)/2}div^t$, $s+t$ is even, – it admits an estimate stronger than "the norm equals one" in $L_2$ with power weight for $s\ne t$, $n>3$ and a suitable interval for the power exponent.
3. The growth of the norm of the operator $D\Delta^{-1}div$ in $L_p$ for small deviations from $L_2$ has the second degree of smallness in $p-2$; similarly in spaces $L_2$ with Muckenhoupt weights.
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