The sup-norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials

Daniel Galicer, Martín Mansilla, Santiago Muro

Let $A_{p,r}^m(n)$ be the best constant that fulfills the following inequality: for every $m$-homogeneous polynomial $P(z)={\sum }_{|\alpha |=m}{a}_{\alpha }{z}^{\alpha }$ in $n$ complex variables, $$\big(…