POINTWISE CONVERGENCE OF ALMOST PERIODIC FOURIER SERIES AND ASSOCIATED SERIES OF DILATES

摘要

Let S-2 be the Stepanov space with norm parallel to f parallel to(S2) = sup(x is an element of R) (f(x)(x+1)vertical bar f(t)vertical bar(2)dt)(2)(1/2), lambda(n) up arrow infinity, and let (a(n))(n = 1) satisfy Wiener's condition Sigma(n = 1)(Sigma(k:n =lambda k = n+1)vertical bar a(k)vertical bar)(2) infinity. We establish the following maximal inequality: