A new class of function spaces generalizing the Arias-de-Reyna space

This paper studies the structure and properties of a rearrangement-invariant quasi-Banach space $Q{A}_{\phi ,\psi }$ which generalizes the classical space $QA$ introduced by Arias-de-Reyna in connection with the study of the pointwise almost everywhere convergence of Fourier series. We present basic properties of $Q{A}_{\phi ,\psi }$ and explore the relationship between $Q{A}_{\phi ,\psi }$ and other rearrangement-invariant Banach spaces.