Conjugate Transforms on Dyadic Group

摘要

In this paper we study the properties of the Lebesgue constant of the conjugate trans- forms. For conjugate Fejer means we will find necessary and sufficient condition on t for which the estimation E vertical bar(sigma) over tilde ((t))(n)f vertical bar = cE vertical bar f vertical bar holds. We also prove that for dyadic irrational t, L log L is the maximal Orlicz space for which the estimation E vertical bar(sigma) over tilde ((t))(n)f vertical bar = c(1) +c(2)E(vertical bar f vertical bar log(+) vertical bar f vertical bar) is valid.