Anisotropic hardy spaces of Musielak-Orlicz type with applications to boundedness of sublinear operators.
Let φ : ℝ(n) × [0, ∞)→[0, ∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, H(A)(φ)(ℝ(n)), via the grand maximal function. The authors then obtain some real-variable characterizations of H(A)(φ)(ℝ(n)) in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space H(A)(p) (ℝ(n)) with p ∈ (0,1] and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of H(A)(φ)(ℝ(n)), and, as an application, the authors prove that, for a given admissible triplet (φ, q, s), if T is a sublinear operator and maps all (φ, q, s)-atoms with q < ∞ (or all continuous (φ, q, s)-atoms with q = ∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from H(A)(φ)(ℝ(n)) to ℬ. These results are new even for anisotropic Orlicz-Hardy spaces on ℝ(n).
School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
Baode
B
Li
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China.
Dachun
D
Yang
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China.
Wen
W
Yuan
D016880:Anisotropy; D016014:Linear Models