Strong approximation via Sidon type inequalities
The authors continue to explore the relation between Sidon inequalities and strong summability. After establishing a duality theorem which serves as a mechanism for translating Sidon type inequalities into estimates of strong means of Fourier series and vice versa, they establish some very powerful, general results about strong summability (including strong oscillation as measured by de la Vallée Poisson means) in a variety of spaces including Hardy spaces and BMO. The methods are so general that they apply equally well to the trigonometric, Walsh, Ciesielski, and UDMD systems.
scientific article; zbMATH DE number 1214026
scientific article