Almost Everywhere Convergent Fourier Series

作者：Carro M J^*; Mastylo M; Rodriguez Piazza L

来源：Journal of Fourier Analysis and Applications, 2012, 18(2): 266-286.

DOI：10.1007/s00041-011-9199-9

• Fourier series
• Almost everywhere convergence
• Lorentz spaces
• Banach envelope
• Rearrangement invariant spaces

We study some properties of the logconvex quasi-Banach space QA defined by Arias-de-Reyna and show several applications to convergence of Fourier series. In particular, we describe the Banach envelope of QA and prove that there exists a Lorentz space strictly bigger than the Antonov space in which the almost everywhere convergence of the Fourier series holds. We also give a necessary condition for a Banach rearrangement invariant space X to be contained in QA. As an application, we show that for some classes of Banach spaces there is no the largest Banach space in a given class which is contained in QA.

• 出版日期2012-4