Two-side estimates for sums of absolute values of Fourier coefficients of functions from H ^ω(T ^m)

Abstract

The class of functions H ^ω is considered, where ω(t) is a continuity modulus monotone in the sense of Hardy and satisfying some condition C. The behavior of the value $\mathop {\sup }\limits_{f \in H_\omega } \left\| f \right\|_{A_p }$ is obtained, where $\left\| f \right\|_{A_p }$ is the sum of absolute values of Fourier coefficients of a function f ∈ L(T ^m) in pth power.