The L(p) version of Newman's inequality for lacunary polynomials Academic Article

The principal result of this paper is the establishment of the essentially sharp Markov-type inequality [ x P ( x ) L p [ 0 , 1 ] ( 1 / p + 12 ( j = 0 n ( j + 1 / p ) ) ) P L p [ 0 , 1 ] |xP (x)|_{L_p[0,1]} leq left (1/p+12 left ({sum ^n_{j=0}}(lambda _j + 1/p)
ight )
ight ) |P|_{L_p[0,1]} ] for every P span { x 0 , x 1 , , x n } P in operatorname {span}{x^{lambda _0}, x^{lambda _1}, ldots , x^{lambda _n}} with distinct real exponents j lambda _j greater than 1 / p -1/p and for every

authors

• Erdelyi, Tamas