MULTIPLIERS FOR NONCOMMUTATIVE WALSH-FOURIER SERIES

作者：Wu, Lian^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(3): 1073-1085.

DOI：10.1090/proc/12831

• Noncommutative martingales
• multipliers
• Walsh-Fourier series

We consider multipliers for noncommutative Walsh-Fourier series. Let R be the type II1 hyperfinite factor. For x is an element of L-1( R), 0 < alpha < 1, the multiplier transformation of x is defined by setting @@@ J(alpha)x = Sigma(gamma is an element of F)2(-gamma(1)alpha)(x) over cap(gamma)omega(gamma), @@@ where (w gamma)(gamma is an element of F) is the noncommutative Walsh system in R and Sigma gamma is an element of F (x) over cap(gamma)omega(gamma) is the Walsh-Fourier series of x. It is shown that @@@ vertical bar vertical bar J(alpha)x vertical bar vertical bar L-1/(1- alpha),L-infinity(R) <= c vertical bar vertical bar x vertical bar vertical bar L-1(R), @@@ where c is a constant depending only on alpha. Via interpolations, we deduce that J(alpha) is bounded from L-p(R) into L-q(R) where 1 < p < q and alpha = 1/p - 1/q, thus providing a noncommutative analogue of a classical result of Watari.

• 出版日期2016-3
• 单位中南大学