Weak Boundedness of Fourier Operators and Conjugate Transforms

Abstract:

      Let S_n(dF, x) be the partial sums of the Fou ier-Stieltjes F(dF) with F(x)∈ BV[ 0.2π].We prove that there exists an absolute constant A such that N₁(S_n((dF, x))v, where N₁(g) =(?)ames [x|g(x)>α].In particular N₁(S_n(f, x))1 for f∈L_2π¹(which is called uniform weak boundedness of operators S_n). The same statement is asserted concerning Fourier-Stieltjes single integrals