Convergence in measure of Fejér means of two parameter conjugate Walsh transforms

Abstract

. Weisz proved-among others – that for f ∈ L log L the Fej´er means (cid:2) σ ( t , u ) n , m of conjugate transform of two-parameter Walsh-Fourier series a. e. converges to f ( t , u ) . The main aim of this paper is to prove that for any Orlicz space, which is not a subspace of L log L , the set of functions for which Walsh-Fej´er Means of two parameter Conjugate Transforms converge in measure is of fi rst Baire category.