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Inequalities for the Polar Derivative of a Polynomial

Complex Analysis and Operator Theory, 2010
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Liman, A., Mohapatra, R. N., Shah, W. M.
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Conjugate Inequalities for Functions and Their Derivatives

SIAM Journal on Mathematical Analysis, 1974
We consider finding the best possible constants $C = C(n,\alpha ,\beta ,p,q)$ such that $\| f \|_p \leqq C(b - a)^{n + 1/p -1/q} \| {f^{(n)} } \|_q $ under several differen sets of boundary conditions. Specifically in one case, f is required to have a zeros at $a $ and $\beta $ zeros at b where $n \leqq \alpha + \beta \leqq 2n$, $\alpha \leqq n$ and ...
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LOGARITHMIC VERSION OF INTERPOLATION INEQUALITIES FOR DERIVATIVES

Journal of the London Mathematical Society, 2004
The classical Gagliardo-Nirenberg inequality \[ \| \nabla^{(k)} u \| _q \leq C \, \| u \| ^{1-k/m}_r \| \nabla^{(m)} u \| ^{k/m}_p \] in \(R^n ...
Kałamajska, Agnieszka   +1 more
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