Yang D., Liang Y., Ky L.D. Real-Variable Theory of Musielak-Orlicz Hardy Spaces

Springer International Publishing AG 2017. — 476 p. — (Lecture Notes in Mathematics 2182) — ISBN: 3319543601.Both the real-variable theory of function spaces and the boundedness of operators are always one of the core contents of harmonic analysis, while the Lebesgue spaces are the basic function spaces. However, due to the need for more inclusive classes of function spaces than the Lp.Rn/ families from applications, Orlicz spaces were introduced by Birnbaum-Orlicz and Orlicz, which is widely used in various branches of analysis. As the Orlicz spaces, Musielak-Orlicz spaces are also defined via the growth functions. Compared with the growth functions of Orlicz spaces, the growth functions of Musielak-Orlicz spaces may vary in both the spatial variable and the growth variable. Thus, by choosing special growth functions, Musielak-Orlicz spaces may have subtler and finer structures, which play a key role in solving the endpoint or the sharp problems of analysis.Musielak-Orlicz Hardy Spaces
Maximal Function Characterizations of Musielak-Orlicz Hardy Spaces
Littlewood-Paley Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces
Riesz Transform Characterizations of Musielak-Orlicz Hardy Spaces
Musielak-Orlicz Campanato Spaces
Intrinsic Square Function Characterizations of Musielak-Orlicz Hardy Spaces
Weak Musielak-Orlicz Hardy Spaces
Local Musielak-Orlicz Hardy Spaces
Musielak-Orlicz Besov-Type and Triebel-Lizorkin-Type Spaces
Paraproducts and Products of Functions in BMO.Rn/ and H1.Rn/ ThroughWavelets
Bilinear Decompositions and Commutators of Calderón-Zygmund Operators