The Lp version of Newman's inequality for lacunary polynomials

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(j + 1/p))) ||P|| Lp[0,1] for every P span{x0, x1,... , xn}with distinct real exponents j 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(j+ 1/p))1/p ||P||Lp[0,1] for every P span{x0, x1, . . . , xn}with distinct real exponents j greater than -1/p and for every p [1, ]. Some related results are also discussed. 1996 American Mathematical Society.

authors

• Erdelyi, Tamas

published proceedings

• Proceedings of the American Mathematical Society

author list (cited authors)

• Borwein, P., & Erdlyi, T.

complete list of authors

• Borwein, P||Erdélyi, T

publication date

• December 1996

published in

• Proceedings of the American Mathematical Society  Journal

start page

• 101

end page

• 109

volume

• 124

issue

• 1