Sergey Tikhonov

We will discuss the concept of the general monotonicity of sequences/functions. Some applications to various problems of harmonic analysis and approximation theory will be considered.

About 100 years ago, William Henry Young and Felix Hausdorff provedthat, for a periodic L_p-integrable function, the sequence of its Fourier coefficients necessarily lies in the discrete \ell_{p'} space provided that p' is the conjugate of p and 1