A sharp discrete Sobolev inequality and left inverses of higher order differences

Raul Hindov, Shahaf Nitzan, Jan-Fredrik Olsen +1

For integers $\alpha ,d⩾1$, we determine the best constants in the inequalities $||(a_j{)}_{j=1}^d|{|}_{{\ell }^1}⩽C_{\alpha ,d}||(({\Delta }^{\alpha }a{)}_j{)}_{j=1}^{d+\alpha }|{|}_{{\ell }^2},$ where $\Delta$ i…