Atomic decompositions of martingale Hardy Lorentz amalgam spaces and applications (Q6548003)

Motivated by the considerable progress which has been made during recent time both in function space theory of amalgam type and martingale space theory, the authors develop the martingale theory in the framework of Lorentz amalgam spaces. Just as Lorentz spaces are generalizations of Lebesgue spaces, Lorentz amalgam spaces are generalizations of Wiener amalgam spaces. The authors introduce the martingale Hardy Lorentz amalgam spaces which are extensions of the martingale Hardy-amalgam spaces. The first aim is to establish the atomic decompositions for these spaces via simple atoms. Then, with the help of the atomic decompositions, the dual spaces of the martingale Hardy Lorentz amalgam spaces are characterized. The second application of the atomic decompositions is the boundedness of the fractional integrals on the martingale Hardy Lorentz amalgam spaces. The author's results are new even for the martingale Hardy-amalgam spaces.