Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators

Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

“…Later, in 1970, Lizorkin [57] further studied both the theory of multipliers of Fourier integrals and estimates of convolutions in the mixed-norm Lebesgue spaces. Moreover, very recently, there appears a renewed increasing interest in the theory of mixed-norm function spaces, including mixed-norm Lebesgue spaces, mixed-norm Hardy spaces, mixed-norm Besov spaces and mixed-norm Triebel-Lizorkin spaces; see, for example, [19,20,30,38,39,40,41]. For more developments of mixed-norm function spaces, we refer the reader to [16,18,27,29,42,43].…”

Dual spaces of anisotropic mixed-norm Hardy spaces

“…However, the aforementioned question on duality theory of H p a (R n ) is still missing so far. In addition, the theory of anisotropic or mixed-norm function spaces was developed well in recent years; see, for example, [6,7,9,14,18].…”

Fourier multipliers on anisotropic mixed-norm spaces of distributions

“…4. Multipliers on anisotropic homogeneous mixed-norm spaces are considered by the present authors in [13].…”