Boundedness of sublinear operators in Hardy spaces on RD-spaces via atoms
By Dachun Yang, Yuan Zhou. 2008
67 citations recorded by the source corpus.
Abstract Let p ⩽ 1 be near to 1 and X be an RD-space, which includes any Carnot–Caratheodory space with a doubling measure. In this paper, the authors prove that a sublinear operator T extends to a bounded sublinear operator from Hardy spaces H p ( X ) to some quasi-Banach space B if and only if T maps all ( p , 2 ) -atoms into uniformly bounded elements of B .
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2875b25526f74c70fbd7f0c35feaf3f68f7b05dc
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Variable Anisotropic Hardy Spaces and Their Applications (2017, unknown): “In addition, for any given γ ∈ (0, 1], a quasi-Banach space Bγ with quasi-norm ‖·‖Bγ is called a γ-quasi-Banach space if there exists a constant κ ∈ [1,∞) such that, for any m ∈ N and {fi}i=1 ⊂ Bγ , it holds true that ∥∥∑m i=1 fi ∥∥γ Bγ ≤ κ ∑m i=1 ‖fi‖ γ Bγ (see [37,78,79]).”
- On Function Spaces with Mixed Norms — A Survey (2019, unknown): “and, for any ψ, φ∈Y , ‖T(ψ)−T(φ)‖Bγ ≤C‖T(ψ−φ)‖Bγ (see [42, 56, 81–83]).”
- Weighted anisotropic product Hardy spaces and boundedness of sublinear operators (2009, background): “The notion of Bγ-sublinear operators was first introduced in [63].”
- Real-variable characterizations of Orlicz-slice Hardy spaces (2018, background): “Next we recall the notion of γ-quasi-Banach spaces (see, for example, [27], [44], [47] and [46]).”
- Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, unknown): “i=1 |μi| ‖T ( fi)‖γBγ and, for any f , g ∈ Y, ‖T ( f ) − T (g)‖Bγ ≤ C‖T ( f − g)‖Bγ (see [81, 82, 44, 79]).”