A Tangential Markov Inequality on Exponential Curves

الأصل · EN

We show that on the curves y=eᵗ⁽ˣ⁾ where t(x) is a fixed polynomial, there holds a tangential Markov inequality of exponent four. Specifically, for the real interval [a,b] there is a constant C such that maxₓ∈ [ₐ,b]|d/dxP(x,eᵗ⁽ˣ⁾)|≤ C(deg(P))⁴ maxₓ∈ [ₐ,b]|P(x,eᵗ⁽ˣ⁾)| for all bivariate polynomials P(x,y).