文摘
This work is dedicated to the investigation of strong summability of Fourier series in the context of periodic Morrey spaces. First, we study the Hilbert transform in the periodic vector-valued context. Boundedness of the Hilbert transform implies uniform estimates of the operator norms of the partial sums of the Fourier series. Afterwards, we study the Lizorkin-Triebel-Morrey and Nikol’skij-Besov-Morrey spaces. Here we concentrate on Lizorkin representations and embeddings into the scale of H?lder-Zygmund spaces. In the final section, we study consequences for strong summability of Fourier series.