ON TWO PROBLEMS OF LEINDLER

Let f(x) be a continuous function with 2π-period i. e. f∈C, and let a/2+ sum form k=1 to ∞ (acoskx+bsinkx) (1) be its Fourier series. S(f)=S(f,x) denotes the n-th partial sum of (1), and E(f), the best approximation of f by trigonometric polynomials of order at most n. L. Leindler in his recent paper raised the following two problems. (Ⅰ) Let p>0 and let r be a nonnegative integer. Is condition