The Lp version of Newman's inequality for lacunary polynomials Academic Article uri icon

abstract

  • The principal result of this paper is the establishment of the essentially sharp Markov-type inequality ||xP′(x)||Lp[0,1] ≤ (1/p+12 (∑j=0n(λj + 1/p))) ||P|| Lp[0,1] for every P ∈ span{xλ0, xλ1,... , xλn}with distinct real exponents λj greater than -1/p and for every p ∈ [1,∞]. A remarkable corollary of the above is the Nikolskii-type inequality ||y1/pP(y)||L∞[0,1] ≤ 13(∑j=0n(λj+ 1/p))1/p ||P||Lp[0,1] for every P ∈ span{xλ0, xλ1, . . . , xλn}with distinct real exponents λj greater than -1/p and for every p ∈ [1, ∞]. Some related results are also discussed. © 1996 American Mathematical Society.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

publication date

  • December 1996