Generalized Hardy spaces
As is known, there are various ways to define Hardy spaces, especially in the multi-dimensional setting. One of such approaches is the maximal function approach. Using it, the authors introduce a family of Hardy spaces based on a functional parameter. Many known Hardy and Hardy-Lorentz type spaces are particular cases. The authors then study interpolation properties of the introduced spaces by the real method with function parameter. Further, they prove the continuity of the Fourier transform of the functions from these spaces and give a control for its growth. They also establish a Hardy-Littlewood-Sobolev type theorem for the Riesz fractional integration and prove the boundedness of singular integral operators.
scientific article; zbMATH DE number 5816585
scientific article